It seems like no police or police report screws them more than it screws you. Way more.
To the point where if they did come after you personally all you have to do is say, "Prove it. Never seen you before in my life." Obviously don't do that... but. Or "Prove it. My insurance companies lawyers have already made the case you're trying to commit fraud."
In this, the ambulance chasers are going after the insurance company because they know that you, Joe Private, are not going to pay out.