I think some of the video sites, like YouTube, have an algorithm that can identify copyrighted music and pull a video down without a complaint.
But, the bottom line here is the police are trying to avoid being held accountable. Think of all the horrible videos we've seen in the past decade that have shown bad cops doing bad things. Arresting people for less than nothing, only to have a video show the cop was lying like a cheap rug. They don't want to be videoed because they know what they are doing is wrong. If they were doing the right thing, I don't think they would have an issue with filming.