Just my humble opinion, but if you recall, the crap in Egypt started much earlier in the day and was really a post 9/11 plus freedom for the Blind Sheik demonstration.
The administration took the party line that it was all about the video just to cover their dealings with the Brotherhood on the Blind Sheik bastard, and then a few hours later all hell broke loose in Benghazi.
They kept the same 'spontaneous lines about the video, and then got caught in a trap that they are still trying to spin their way out of.
I think you have the right idea that Obama didn’t want anything to get in the way of his claim that he helped the Arab Spring and that the Arab Spring was all sweetness and light, but I’m still curious as to how an obscure video trailer that had only about 10K views on YouTube was tapped as the scapegoat for the terrorism.
I’m sure you could point to any number of anti-Muslim videos on YT with many more views and notoriety than the one they picked.
I recall that a spokesperson (maybe the PM himself) of Egypt even denied that the video had anything to do with the protests.
What was it about this particular video that it was tapped so quickly?