Halle Berry defines herself as black woman. I'm pretty sure Alicia Keys does too.....but guess what. That's probably how they were treated growing up. If there was a line for blacks and a line for whites, which one do you think they were closest to?
Same with Obama.....Obama LOOKS black. There's nothing about him that screams mixed.....I know mixed people darker than him.
Black people aren't immune to incorrectly defining a mixed person as black, HOWEVER, white people are the ones responsible for making it a problem/issue with segregation, racism, etc.