I think we have to accept that we're talking about generalities here. Of course, white people don't necessarily enjoy ALL the white privileges ALL the time, nor are ALL black people oppressed in EVERY way ALL the time.
Yes, a smartly-dressed Will Smith is probably a little more likely to be admitted to a swanky Hollywood nightclub than I (an average-looking, middle-aged white comparative nobody).
And, of course, it's not always easy to completely unpick economic and class factors from race as such. (The hypothetical Smith example may be a good example of them overriding race, in fact.)
But...if one looks hard enough there are exceptions to almost every statement. That doesn't mean there isn't a core of truth to the generalisation.
As long as we're not obsessive about insisting it applies to literally every person in every conceivable situation, it's still valuable to be aware that it VERY OFTEN applies, no?
(Apologies for the capitals - I'm not shouting but I don't know how to do italics in these comments, or if you even can.)