First, SJA quotes don't count.
Then, we don't know how/why regeneration works. Is the look you get dependent on genetics? environment? ancestors?
Considering there is no real consistency among the various incarnations of the Doctor and the Master, I don't think there are any pre-existing conditions which determine how a Time Lord's new appearance will be following a regeneration. And furthermore, skin colour isn't exactly uniformly black and white. Some white people have darker skin than other white people, and some black people have lighter skin than other black people. There are so many variations of skin colour within the types classified as "black" and "white" that it kind of makes little sense to dwell on colour any further than if you had to make a description of a person and you wanted details as full as possible.
If the Doctor became a black person, I would see nothing wrong with that and would not consider it a violation of anything previously established. Hell, both the Ninth and Eleventh Doctor's have implied that regeneration can result with a body looking completely different than the standard human/Gallifreyan norm. If it's possible for a Time Lord to regenerate into a body with two heads or none, then it's possible for a Time Lord's skin to change colour.