Sure, and there are thousands of cartoons making fun of Islam - only the ones in Denmark got the attention of the Muslim world for.... what? 6 months?
Your understanding and correlation of "very amateur video", popularity, viral capability, and what is considered amateur is weak AT BEST.
1. Half the horror movies today are filmed at a fraction of the cost of most Hollywood movies (some for $60,000). They get the attention of millions around the world. How are they made? Handheld cameras, nausea inducing editing and unknown actors. Profit? 1/4 of a billion dollars for some.
2. Today, a 7 second video made by kids in Australia can reach North America and get 30 million views in about 2 days. That's kind of the thing about globalization and overpopulation. Salman Rushdi's book took years to write and made its way across the Atlantic in months, a video made in 20 mins insulting Mohammed can do it in seconds.
3. Religions get offended over whatever they want to get offended about. Happy holidays, Christ in piss, Buddha sucking off Vishnu - whatever.
The point of all this is that your argument that there is no way the administration could have thought the video was the cause is beyond ridiculous. Of course they could have. Hell, it wouldn't be the first time Islam gets its panties in a wad over media depicting Mohammed badly. The demand by the white house to take down the video? Perfectly plausible if the narrative is that there was an initial confusion over the cause of the riots. Highly implausible if the narrative is some big giant conspiracy :shrug: