After she shook Kennedy's hand, the natural progression would have been to shake Obama's hand. Rather than shake her hand, Obama appears to have turned away. If Obama hadn't turned away, then Clinton would have been borderline rude to not have offered her hand. Clinton wasn't going to "chat" with Kennedy - it was too awkward of a position to hold for any length of time.

So, I expected Obama to stand there while Clinton shook Kennedy's hand and be ready to offer his hand. Good manners is pretty simple.