1) In Airo and elsewhere there were protests related to the film
2) The attack in Libya.
The President and SoS needed to deal with both in real time. The statements by both on the film were very good - explaining and defending the unusual scope of freedom of speech in the US to peoples who were in lands where no film like that could be made without the government condoning it. It was imperative that they respond as they did -- and it is still something Americans (ie Kerry in Germany) are questioned on.
To understand how mystifying and how troubling people in other countries could find it, remember how many long time ACLU supporters were horrified that they backed allowing the march of neo-Nazis in Skokie, an lllinois town with many survivors. Just as they thought the government should stop it, people in the Middle East questioned if the US government either condoned (or even helped) the film - mystified that if it disgusted us (which it did), it would not be made.
I don't remember the context of the mention of the film by Rice. If the question was specifically Libya, she was wrong to cite that - or anything - as motivation. It would have been better to refer to the investigation that had been started. One question that history might uncover is if the State Department or the re-election campaign suggested mentioning the movie. If this was Rice on her own, she is the one who gave the Republicans an opening.
Leaving alone politics, now and 2016, it will be interesting to learn when accounts are written of the Obama years long in the future, why Susan Rice was placed in that position. Was it to intentionally have someone with no first - or likely even second - hand information - giving them deniability? Was it to not make it a bigger story which putting Clinton on would have done - just because she is Hillary? Was it a test to see if she could navigate a tricky story? At any rate, it does not change what Obama said - the story was out there.