One might be tempted to say the same for you.
She comes from a different set of circumstances and different background. Her view of race is different.
That does not mean that her view of Obama centers around his race.
She made a comment about his race, her views concerning his race are different from yours, obviously, but it does not automatically follow that ALL of her opinions on Obama are centered around his race.
IOW, not as exclusively black. Some people have more distinctions where race is concerned. Personally, I don't even try to guess anymore. I say what color if it's important (light tannish whatever), but I avoid trying to nail down someone's race, because people today are so mixed, it's pretty hard to get it right.
Just because you or society see things one way doesn't a. make it right or b. make any alternative wrong. It's interesting because it almost seems as though you're trying to make people adhere to the old standards, which were, imo, rediculously vague.