That is one hypohesis. I am not convinced of it. Anyone can verify for himself that Arawak Indians living in the equator are much lighter than the Africans living in the equator. Similarly the Eskimos live farther north than the Swedes, yet the Eskimos are darker. Whichever the case 2,000 years are not enough. The Afrikaners have lived in South Africa for 400 years and they as white as the Dutch living in Holland.
Secondly the black African Jews are not merely dark-skinned. They have Negroid facial features. When I speak of "Negroid features" I am not talking of skin color. The people of India are brown-skinned but they are Caucasoid.
As I've written before, sometimes, but not always, you can distinguish physically between Ashkenazi and Sephardi Jews. But among ourselves, the only difference- that counts- is certain difference in customs. For example Ashkenazi Jews don't eat corn on Passover, the Sephardi do. Neither of us denies the descent or legitimacy of the other.
Afrikaaners live at a latitude where "light" skin can be maintained - they are hardly Central Africans.
The vitamin D thing kept human beings from living North of the 30th parallel until they had developed a way to acquire sufficient Vitamin D from a very, very, very extensive fish diet. Eskimos are among those who developed such a diet - including the eating of raw sea mammal livers - a major source of Vitamin D. Quite possibly their darker skinned offspring didn't die in infancy from rickets. As far as Arawaks being lighter than Central Africans, it is suggested that the Arawaks are recent arrivals to their present territory, plus they, like all other persons of predominantly American Indian ancestry, are of mixed European/Indian descent.
Again, there's a lot of this stuff on the net.