So what you are saying is, the police officer should start following that provocateur around on his day off with a camera? Film the guy who is filming the police officers! I like it!
If you antagonize and film a police officer while they are off-duty, that is inappropriate; potentially stalking and harassment. Same in the other direction. The courts have thus far determined there are specific rights to filming police while engaged in their duties; not just for press, but for citizens in general.
Filming: https://en.wikipedia.org/wiki/Glik_v._Cunniffe
Antagonizing: https://www.wired.com/2013/01/flipping-off-cop-case/
If they feel the least bit threatened, they can simply arrest someone who is “stalking” them.
That they are resorting to clever tactics like playing copyrighted music, shows that legally speaking they can’t do anything else.