True, indeed. If you want, you can somewhat prevent.

Although, to be honest, typically videos are buffered and even cached from the browser, so logging incoming web traffic won't help there.

Preventing outgoing traffic might help. Preventing storage would be interesting. I think those machines need to be really just terminals where you can't do literally anything but click yes/no and go to the next in the queue. It'd be interesting to know how they do it.