The issue, in a nutshell, is the GOP claim that the Administration has a habit of trying to associate a portion of the responsibility for terror attacks to America's own behavior. If Obama truly had no information, then he simply assumed that the attacks were in response to the video, and that supports the Republican argument that Obama has a "Blame America" assumption. If he really didn't know, then he should not have mentioned the video.
But that is true. Part of why they attack us is our own behavior. So Obama would be correct in bringing that up. Now it doesn't mean our behavior actually is bad but it is why they attack us.
Let me clarify. The GOP argument is that Obama associates a potion of the responsibility for error attacks on American behavior that Obama thinks Americans shouldn't do.
So when Obama says (according to GOP interpretation of his statements) we should respect Islam, implying that our disrespect is a cause of the attacks, he is saying Americans should treat Islam differently than other religions. (For instance, by not drawing cartoons of Mohammed, and not making disrespectful movies in which Mohammed is a character.) In other words, form the GOP perspective, Obama is not raising American's behavior as explanation but as a partial exculpation.
And in the context of the Rose Garden comments, that's a perfectly valid (not not exclusive) interpretation. Rather than blame the terrorists solely for the attack, Obama interjected a statement about not doing things to disrespect other people's religions, which, in context can only refer to the anti-Mohammed YouTube video that, at the time, some people in the Administration had said triggered the attack. There is no reason to bring that up unless he is saying that we shouldn't be disrespectful about Islam because they might try to kill us for it.
It can be seen as a "Blame America" attitude, particularly when the actions that are being blamed are private citizens' actions that fall squarely within permissible behavior. If Obama were blaming, for instance, past US government actions (like America's past support for regional villains like the Shah, Saddam Hussein, and Mubarak), that would be more appropriate. (It would also have been nonsensical because nobody thinks those to be significant factors.) Rather, he is raising things that Americans sort of think are their Constitutional rights, such as being allowed to ridicule other people's cherished beliefs. And he's not doing it to educate Americans about the Middle East. He is doing it, so the GOP interprets it, to spread the blame, to say "Our hands aren't clean". And that's a strong emotional argument in their favor, if they can convince the American people to interpret the President's statements that way.
Now, Obama can certainly explain away these statements, but the more times he referenced American behavior when discussing violent attacks against Americans, the more the GOP story is going to stick and the less the Democratic position will sound palatable.
Fortunately, Romney bumbled the attack in debate two. We'll see if he correct sin debate three, or if Obama is able to turn it around.
