There's no way to know. It crossed my mind too to wonder about that. I would like to think that an African-American man, or woman!, who had done all the same things would have wound up in the same position. But I don't know that we're there yet.
The problem I have with invoking "white (or male) privilege" is that it tends to depreciate the person's accomplishment, and even to make them feel guilty for it. If they have done something to demonstrate prejudice or encourage it in others, that is fair game for criticism. Succeeding at something, in and of itself, is not, even if you think it was easier for them than it should have been.