The verse mentioned above does not say that white people are better than other races, actually it has nothing to do with the abovementioned issue, the words used in the verse may seem to relate to races but they have a meaning other than being black and white. In Arabic people who reach salvation and prosperity are called "white faced people" and those who do not are called "dark/black faced people", these sorts of expressions and other similar ones such as “a dark heart” or “the night was pitch black” that have nothing to do with races are not only found in Arabic, but in other languages as well.
In respect to the hadith cited above, aside from the fact that some parts of it aren't in conformity with Islamic teachings, and its chain of narrators isn't a decent one, making its authenticity disputable, we must pay attention to the fact that although youth, health and beauty aren’t of Islam does not deny that white skin is more beautiful and attractive, but it denies the notion that being white is a spiritual advantage and value; therefore it makes complete sense for black people to turn white when entering heaven. Add to above that this hadith is not considered authentic.
Prior to answering your question I would like to ask what is understood by a sentence like this: "The whiteness of the day guides you better towards your goal than the blackness of the night". Would you consider such a sentence offensive to black people? What if it is said: "By using this medicine or makeup, bring youth back to your face", will you assume the sentence is trying to disrespect elderly people?!
Obviously the answer is no, because the whiteness or black color of the night has nothing to do with races. Although most people prefer having white skin but being white is no spiritual value or advantage, therefore we believe many black people who possess human values and act according to them are much higher and respectful then white or beautiful individuals who do not.
Taking into consideration what was said above, we will answer the question in two parts like it was asked, one regarding the hadith and the other regarding the verse:
Part One) Verse 106 of surah Ale-Imran
It seems that there may have been a misunderstanding here, maybe because the expresssion "Black-faced" has a different meaning in Arabic and Farsi and most people are unfamiliar with these languages. The points explained below will help us comprehend the true meaning of the verse.
There are many verses in the Quran which clearly explain that despite the differences that are found among humans, they are all from the same root and nothing will make one more valuable or respectful other than his righteousness and piety, let it be physical features, family ties or gender, some of these verses are as follows:
1- "O mankind! Indeed we created you from a male and a female, and made you nations and tribes that you may identify yourselves with one another. Indeed the noblest of you in the sight of Allah is the most God wary among you."
2- "O mankind! Be wary of your Lord who created you from a single soul, and created its mate from it, and, from the two of them, scattered numerous men and women. Be wary of Allah, in whose Name you adjure one another, and the wombs. Indeed Allah is watchful over you"
3- "It is He who created you from a single soul"
These verses that being white or black is no true supremacy or advantage. Even when we look back on the lives of prophets and those who lead the Muslim society we find that black and white have worked hand in hand and stood at each other’s side to spread the word of Islam.
It is very unlikely for someone to be familiar with Islam, and not know that the Bilal was the prophet’s (pbuh) mu’adhin (caller to prayer)!
Not to deny that there were Muslims who assumed they were better than black people as a result of them still bearing some of the jahiliyyah ideology they had before Islam, but such a point of view has always been rejected by Muslim leaders.
When the Prophet addresses the people of his time he says: "O people! All of you have one God, and your father Adam and your mother Eve were created from dirt. (Therefore) The most noble of you in the sight of Allah is the most pious of you".
Imam Ali would equally pay people their share which was three "dinars" from the "Beitulmal" (the treasury). A man from the Ansar came to him and received his three dinars and then a black person came and received the same amount of money.
The man from the Ansar was surprised and protestingly said: "Up until yesterday this black man was my servant, does it make sense for me to get as much money as he does?!" The Imam replied that the argument had no reasoning and that none of the two was higher than the other."
In a similar story the Imam faced his brother "Aqil" that said: "Do you think my share equals the share of a black man?!" The Imam strongly denied such a notion and replied: "It is only if you are more righteous and have done more for Islam that will make you more respectful and valuable, otherwise you are completely equal to him."
Therefore no fair person can deny the fact that Islam has strongly opposed segregation and prejudice, and this is exactly the reason why some of the wealthy and rich opposed Islam and denied to embrace it. Some of them would ask the prophet to isolate and leave the poor to themselves, making this a condition of their embracement of Islam, but Allah (swt) revealed a verse and ordered the prophet (pbuh) to reject such an offer.
Even if you examine the Quran and all Islamic sources, you will not be able to find one case where a black man or an individual from another race has been completely or partially denied of his right of ownership, marriage, employment, heritage and etc… because of being black; on the contrary, he has the same rights white people do. There is also no teaching saying that the reward or punishment of a certain deed is allocated to the white or that one can reach and possess higher levels of spirituality solely due to his color or race.
Now we need to look back on the verse you asked about to understand exactly what the verse is telling us, and find out why black faces will be punished and the white faces will be rewarded with paradise.
As we explained before, being black can have two meanings. In Arabic and Farsi being black or black faced has a second meaning which refers to those who haven't reached salvation, let the person be physically white or black. On the other hand a person who reaches salvation and prosperity is referred to as a white person even if he is black. We read in the Quran:
"And when a daughter is announced to one of them, his face becomes black and he is full of wrath"
We all know of the ignorant tradition of having hate for female newborns that Arabs had before Islam, which were definitely not black, but still the word black is used in the verse to refer to them, so the word is used in a different meaning, as explained above.
Again while examining the Quran we come across a verse in which Allah addresses his prophet saying: "And on the Day of Resurrection you shall see those who lied against Allah; their faces shall be blackened"
Obviously "those who have lied against Allah" can be from any race and color, so the fact that their faces will turn black has nothing to do with black skin color, but rather relates to their fate and whether or not they will reach salvation in the hereafter.
We also see this word in Farsi poems where they are definitely used in a meaning that has nothing to do with having black skin: "Those who trick others will turn black"
Of course there are many other examples, but what was said seems sufficient enough to get the point across.
It's interesting that sometimes being white is not a value and actually being black is better, in the word of the Almighty when Prophet Yaqub loses his son Yusuf: "His eyes became white on account of the grief", here being white is no good even from a physical and unspiritual point of view.
Therefore using words like black and white are not used to praise or offend a certain race or color of skin, and if one claims that they seem racial he should not use phrases like "the black night" "the whiteness of the day" "a black and darkened mind" because they too can be implicative of races.
Add to the above that the Arabs who were directly addressed by these verses were not totally white like the Europeans, and their skin color was relatively dark, so they could not even be proud of their color either, they even called the people of Rome the "Bani al Asfar" "Yellow People", because the people of Rome had whiter skin than them!
If being white was a sign of one’s value and respect in the sight of Allah, then the prophet should have been more white than any one else, but he was actually tan-skinned. When looking back on history we find many other spiritual individuals that were not white, a good example would be Luqman the Wise, there is a surah named after him in the Quran which mostly contains his advices to his son; according to one narration he was a black servant that was born in "habashah", currently known as Ethiopia.
Therefore the reason why the Quran has used such words to explain what will take place on the day of Judgment is because it is revealed in Arabic, and as we explained before these words have nothing to do with the color of one’s skin, but relate to the fate and destiny of the person, if he is reaches salvation he is called "white faced" and if not he is referred to by "black faced".
Part Two) The hadith referred to in the question
Regarding the hadith mentioned in your question, we must explain that it seems that the sheikh was speaking about a hadith in which the prophet tells an old woman from the tribe of "Bani Ashja’" that old women will not go to heaven, so she went to a corner and began weeping, then "Bilal", the prophet’s "mu’adhin" came along and asked for an explanation from the prophet, the prophet then informed Bilal that black people will not enter paradise either, he also joined the old woman in weeping, after that "Abbas" the prophet's uncle passed by and saw them and tried to help, this time the prophet said that old men will not go to paradise too, so he also like the rest began crying. Then the prophet came to them and let them know what he had truly meant by what he had said and that he was just joking with them. He said: "All good people will enter paradise in the best and most beautiful state possible, and their faces will turn young again" he then pointed out that those who go to heaven will have no body hair, and not even beards and mustaches.
Now we will observe the hadith in terms of the chain of narrators who have cited this hadith one after another and in terms of the meaning of the hadith itself.
1- It must be noted that this hadith has not been narrated in any authentic book, and you will not find it any of the four authentic Shia hadith sources.
Nevertheless one of the scholars who lived in the fifth and sixth century named Ibn Shahr Ashub has narrated it but has not mentioned a chain of narrators, not even a chain that isn't authentic, later on this hadith has been cited in books like Biharul-Anwar and Mustadrakul-Wasa’el in the same form.
Therefore from the viewpoint of Islamic scholars this hadith is considered Mursal (making it unauthentic) and referring to it is not accepted.
2- Some Mursal hadiths are accepted in the study of hadiths (ilmul-hadith) because of their comformity with Islamic teachings and rulings, in other words the content of the hadith makes up for it's unauthentic chain of narrators.
Now we will examine the content of this hadith:
The content of the hadith is comprised of several parts that each must be dealt with and judged about separately.
a) The first part of the hadith is unacceptable because it is very difficult to believe that the prophet would upset and bother others through joking even for a small period of time to the extent that they would cry, especially that he is known as a good role model for the believers in the Quran. Also, history tells us that Abbas the uncle of the prophet was not much older than the prophet himself, so Abbas could respond that if old men don't go to paradise than you yourself won't go either! On this basis, the first part of the hadith contains clues that suggest its inauthenticity.
b) But we can still believe in the second part of the hadith and the fact that old people will turn young, black people will turn white and handicaps will be cured are definitely not considered in any way offensive to them.
Those who still think that black people and other races are less respectful and less valuable and therefore have less rights than white people, will be criticized by people around the world and will eventually cease to exist as was the case with the government of South Africa. There is no such a thing in Islamic teachings and such a notion is utterly rejected. Nevertheless, if someone says that white skin looks better than black skin, it can't be considered some sort of “apartheid” and prejudice and that is why you can never find a human rights convention resolution that says all people around the world are equal in looks. It is clear that certain races might be better looking than others, the same way some white people are more better looking than other white people. Therefore it is completely reasonable to believe that all humans who go to heaven will turn white, and not only that, but will enter paradise in the most beautiful state, with no signs of oldness or being handicap and with no extra hair or body odor, there they will all start a new and everlasting life.
It seems obvious that such a description of people who go to heaven can not be conceived as offensive to their pasts in this world; all of this is trying to convey that they will be the best looking they can be.
We should always keep in mind that there are chances that many of the good looking people in this world will be punished in Hell and that a vast majority of humans who may not be that good looking in this world will live in heaven forever.
"یا أَیُّهَا النَّاسُ إِنَّا خَلَقْناکُمْ مِنْ ذَکَرٍ وَ أُنْثى وَ جَعَلْناکُمْ شُعُوباً وَ قَبائِلَ لِتَعارَفُوا إِنَّ أَکْرَمَکُمْ عِنْدَ اللَّهِ أَتْقاکُم"
 "یا أَیُّهَا النَّاسُ اتَّقُوا رَبَّکُمُ الَّذی خَلَقَکُمْ مِنْ نَفْسٍ واحِدَةٍ وَ خَلَقَ مِنْها زَوْجَها وَ بَثَّ مِنْهُما رِجالاً کَثیراً وَ نِساء "
 " وَ هُوَ الَّذی أَنْشَأَکُمْ مِنْ نَفْسٍ واحِدَة "
Tajuddin Al-Sha’iri, Jame’ul-Akhbar, pg. 183.
 Muhammad ibn Yaqub Kuleini¸ Kafi, vol. 8, pg. 69, hadith 26.
 Ibid, vol. 8, pg. 182, hadith 204.
 "وَ لا تَطْرُدِ الَّذینَ یَدْعُونَ رَبَّهُمْ بِالْغَداةِ وَ الْعَشِیِّ یُریدُونَ وَجْهَهُ ما عَلَیْکَ مِنْ حِسابِهِمْ مِنْ شَیْءٍ وَ ما
ِنْ حِسابِکَ عَلَیْهِمْ مِنْ شَیْءٍ فَتَطْرُدَهُمْ فَتَکُونَ مِنَ الظَّالِمین"
 "وَ إِذا بُشِّرَ أَحَدُهُمْ بِالْأُنْثى ظَلَّ وَجْهُهُ مُسْوَدًّا وَ هُوَ کَظیم "
 "وَ یَوْمَ الْقِیامَةِ تَرَى الَّذینَ کَذَبُوا عَلَى اللَّهِ وُجُوهُهُمْ مُسْوَدَّةٌ "
 "وَ ابْیَضَّتْ عَیْناهُ مِنَ الْحُزْن "
 Muhammad Baqir Majlisi, Biharul-Anwar, vol. 16, pg. 144. In Arabic,
he term “al-asmar” is used to refer to tan colored people.
 Biharul-Anwar, vol. 13, pg. 423.
 Muhaddith Nouri, Mustadrakul-Wasa’el, vol. 8, pg. 410, hadith 9826.
 " لَقَدْ کانَ لَکُمْ فی رَسُولِ اللَّهِ أُسْوَةٌ حَسَنَةٌ لِمَنْ کانَ یَرْجُوا اللَّهَ وَ الْیَوْمَ الْآخِرَ وَ ذَکَرَ اللَّهَ کَثیرا"