But like you said, they lied about you provoking them and destroyed the evidence showing that you didn't. Nobody will ever know that they beat you up just because you were recording.
I know why cops don't want body cams.
> You may have a chance to see justice because it won't matter if the cop and his 5 buddies say you provoked them with a camera. It's unambiguous that you can record them and there's no possibility of reasonable doubt if you're allowed to record them 100% of the time. There's no loophole they can use to say you can't record them due to privacy or safety or whatever other reasons they want to make up and they'll be in the wrong the second they take action against you.
There won't be a lie they can spin because they won't have any justification for attacking a cameraman. Note I also said may and spoke of probabilities. Furthermore, I admitted it's only a partial solution so I'm not sure what gotcha you're going for here. I know it's not foolproof or perfect, it's merely better than what we currently have.