<<Then how is that "staying true to who he is"?>>
It's a subjective feeling. Sorta like hippies in the Sixties trying to get away from their "materialistic" or "plastic" home environments and getting back to the land.
Maybe "being true to who he is" isn't the best way to put it. Maybe it's more like "getting back to who you were supposed to be."
Maybe he feels, or a lot of urban, up-scale blacks feel, they sacrificed too much of their "selves" to get to where they are now and they need to get back to their roots.
Maybe a lot of blacks "recognize" something in the ghetto, something that the more assimilated world of the black suburbanites have had to lose, but that reminds them of home, or grandparents or elderly aunts and uncles.
I can recognize a cadence in Obama's voice that is not there in the voices of white suburbanites, usually in the way he says "y'know," the "y" sound followed closely by the "o" in know together almost making a "yo" as in, well, as in "yo muthafucka." Maybe he just wants to be able to say "yo" without evoking scary gangsta images in white imaginations.
All I know, bottom line, is that there's a comfort level for folks who have to assimilate into a larger society, where they keep enough of what they were raised on or are familiar with to be comfortable, and not too much which would mark them as an outsider. And if they keep on too much of the old stuff, they are just never going to fit in, and if they leave too much behind, they are just phonies. So a black always has a comfort zone where he knows he's not "acting white" and he's not embarrassing himself in the larger society. And a black can usually tell if he feels another black is "acting too white."
My guess, and it's based on some of those "y'know's" that I heard, is that Obama, whether raised in the ghetto or not, has a comfort level that includes some of the ways of speech of the less assimilated black community and could easily and very comfortably lapse into it. And there is some degree of discomfort when he's out of it.