One theme of the book is that we can't excape being identified by our skin color. Yet, at the same time, our skin color does not necessarily dictate that we retain the social attributes that are stereotypically liked with our "race". The may socially exclude us from said group.
Complicating the situation further is the question of how much our skin color relates to our experiences shaping who we are. One example Copland used was that of blacks not tipping. If there is an assumption that black people won't tip, then they may get poor service. Receiving poor service, they may indeed be less likely to tip. This cycle creates a "chicken-or-the-egg" delima which makes it difficult to devide truth from fiction and fuels a self-fulfilling prophesy.
Brian in a sense does not identify himself as a genuine black man because he does not share a similar background/lifestyle (in many respects) or a similar philosophy or values system.