Did Petraeus lie to the House Intelligence Committee in the hope of keeping his job?

And did the Obama administration take advantage of that hope then oust him when the election was over? That's what Charles Krauthammer thinks.

Petraeus told the committee (on September 14th) that the Benghazi attack arose out of spontaneous protests over the “Innocence of Muslims” video. His prestige gave great weight to the administration's story in those key days after the attack. That testimony, Krauthammer says, is "the thing that connects the two scandals, and that’s the only thing that makes the sex scandal relevant."

Otherwise it would be an exercise in sensationalism and voyeurism and nothing else. The reason it’s important is here’s a man who knows the administration holds his fate in its hands, and he gives testimony completely at variance with what the Secretary of Defense had said the day before, at variance with what he’d heard from his station chief in Tripoli, and with everything that we had heard. Was he influenced by the fact that he knew his fate was held by people within the administration at that time?...

Of course it was being held over Petraeus’s head, and the sword was lowered on Election Day. You don’t have to be a cynic to see that as the ultimate in cynicism. As long as they needed him to give the administration line... everybody was silent. And as soon as the election’s over, as soon as he can be dispensed with, the sword drops and he’s destroyed....

Krauthammer's theory contains the assumption that the administration didn't need Petraeus anymore after Election Day. Yet the very statement of the theory hurts the administration, and that injury only occurs because they did drop the sword on Petraeus. The administration still needs to get through its Benghazi problem. This presents a puzzle. What's the advantage in exposing Petraeus now? Perhaps the idea is for him to embody the misbegotten "Innocence of Muslims" story, which is now rejected. Others who passed that story along — notably Susan Rice, who may be the Secretary of State — can be restored to health after the surgical removal of the Petraeus cancer. Rice's conspicuous Sunday show appearances took place on the 16th. She said:

Based on the best information we have to date ... it began spontaneously in Benghazi as a reaction to what had transpired some hours earlier in Cairo, where, of course, as you know, there was a violent protest outside of our embassy sparked by this hateful video. 

Based on the best information... Make that Petraeus... and now he's gone. Except he's not gone. He's the most conspicuous man in the world right now. The cancer on the Presidency is lying exposed —  grisly and repulsive — on the surgical tray that is the media.