> I am guessing because filing a fake police report is a crime...
No. In Germany, many left-wing activists do not file police claims if they've been beaten up or assaulted by fascists. The problem is that the police gives the opposite party or at least their lawyer the full address of the victim - and these addresses tend to be aggregated and leaked on fascist blogs.
In America, where even private information such as divorce papers apparently falls under "this is a public document" rules, I wouldn't even dare calling 911, much less filing a police report.