Shaker heights was full of affluent African Americans, and yet there was still a large acheivment gap between the black students and white students. The study concluded that the parents didn't involve themselves in their children's education as they figured living in an upper middle class society did the work for them. Meanwhile the kids held themselves back so they wouldn't be "acting white".
You can read about the study here, it's quite facinating:
http://www.racematters.org/whyareblackstudentslagging.htm
For what it's worth, I'm black and grew up an upper-middle-class household in a mostly white middle-class area. At 27 I've had no trouble finding a good job and in fact just recently turned down a high-paying job offer at a fortune 500 last month. Race has never been an issue for me, one way or the other.