I agree with the bulk of your post.
But there was NO PROTEST period.
So why push that agenda for 2 weeks?
CNN itself reported on Sept. 20: "The White House,
for the first time Thursday, declared the attack that killed Stevens and three other people a terrorist attack."
bold added by me.
According to a review of briefing transcripts and administration statements, senior Obama administration officials strongly alluded to a terrorist assault and repeatedly declined to link it to an anti-Muslim video that drew protests elsewhere in the region, then suddenly a new narrative emerged Sept. 16 when U.S. ambassador to the United Nations Susan Rice asserted in a series of TV appearances that the best information available indicated that the attack had spun off from a protest over the video.
Why the change? No one really has answered that question, but in the end it came to light that there never was a protest, so THAT seems strange at the very least.