But Charley raised a good point. That film serves Al Qaeda's purpose perfectly. So why they haven't ever made one like that?
Maybe they really are sincere Muslims (not just political opportunists like Bush minimus) and wouldn't be able to take part in making a film derogating Muhammed no matter what the reason or intended effect.
Or maybe they would consider it cowardly to pretend to be someone else and not take credit for their actions. I assume Charley meant that they could make a film like "Innocence of Muslims" but pretend it was made by American Christians or Jews. Otherwise it wouldn't undermine American good will.
If they didn't mind doing it covertly, and if they were really clever, they would first pretend the film-maker was Jewish, using a thinly veiled lie that could easily be exposed, and then fall back on a better-documented lie that he's Christian. After exposing the first lie, everyone would assume they'd uncovered the truth and wouldn't question the second lie, even after the film-maker's alleged church denied it, and even though he's obviously an amoral sleezeball who could be hired to do anything for money.