Barack Obama and the Ambiguity of White Privilege

In this video clip, Barack Obama gives a speech on the issues of racism he's faced in his presidential candidacy. He addresses everyone in the diverse country, bringing issues to the forefront that effect everybody in the same ways. From health care to the war on terror, he addresses the people of America in an even and equal fashion. He talks about his own background, of having a black Kenyan father versus a white family on his maternal side. In this, he embodies the essence the opposes exactly the idea of white privilege. In his upbringing, does Obama not admit that he experienced the positive effects of white privilege? He talks of the positive experience he's had growing up with a white mother and a white family, and he contrasts this sharply with his experience of living in Kenya, which he refers to as one of the poorest countries.
If an African American man can experience the benefits of white privilege, does that not show the ambiguity of such a concept? Is it due to his multicultural background or his obvious affluence that allowed him the ability to grow up in an environment where running for President would be a possibility for him? Either way, Barack Obama is an example of an exception. Of course, he is not completely free of racism, since becoming a public figure, he's experienced more than his share of it, but that's not to say that he has not experienced the positivity as well.
             In fact, at the 20:33 mark he discusses something he refers to the "immigrant experience" and in contrast to the typical image of an immigrant, he is discussing the struggle of the middle class white population. He talks about the anger of the white population, over the things that are taken from them and given to other people, because of their majority status. He is able to see different sides of the issue of Racism, admitting to experiencing both sides of both the black and white struggle. As a man who has seen both sides of the struggle, he's the perfect example of an African American man who has experienced the so called "white" privilege. Does this not change the issue of "white" privilege to one of class privilege? Its ambigious nature, including and discluding people not because of thier skin colour but because of their status brings discomfort to the issue.