Way back when you were considered black if your blood was only 1/6 or 1/8 black (Can't remember the exact fraction). But basically even you didn't appear darker skinned you were still considered of Negro heritage.
We have come a little ways from that point in that we don't go strictly by heritage, but we still pretty much go by appearance. So while Obama may not be as dark as Wesley Snipes, he is dark enough, with enough heritage for many to call him Black. And in the PC world, Negro/Black = African-American.
Whether any of this is right or wrong or even the right attitude to have was not my intent to prove or disprove, simply my opinion/answer to the original question.