With the arrival of the Adobe Creative Cloud — thanks for telling me, jerks! I was able to put a background in a short video I produced using the YouTube video editor.
It is composed of things that spin in the same manner as a record playing, against a green screen. The music is by Basement Jaxx.
The original green screen version is still up on my YouTube channel. It is less fun to watch. The bright green screen in the background is just unpleasant. I would imagine the video could be quite easily ripped off the Internet somehow, in order to give it ones own background footage in a new video remix.