There's a difference though from talking about a shared Anglo-Saxon heritage between two countries and saying Obama doesn't understand that heritage. Why would Obama as a fellow American understand that heritage any less than Romney?
Because he's a retard.
More to the point, Obama is an educated gentlemen and he SHOULD understand that heritage. However, it has been clear from some time (as evinced by his previously cited snubs, his apology tours and his general willingness to talk of American ideals as outmoded concepts) that he considers that heritage to be unimportant or even negative.
Again, a president who "understands" that heritage wouldn't crap on it by treating British leaders which such obvious disdain.
Pure speculation on my part but there is also the fact that Obama's dad was Kenyan. I would hardly be surprised to find out that his father, perhaps with some justification, viewed the British with resentment over the colonialism. That could have easily rubbed off on the president.