I'd think that the selection bias would make far it easier to remember the positive events in this situation. This event would not have made the news, and no one would have been aware of it except for the victim if the police chief hadn't raised an (apparently huge) stink. If it's difficult for the Nashville chief of police to get traction on an incident that happened within his jurisdiction, what chance do you have?

Not really. Negative and positive events do not balance each other out. If your local authorities go help kittens out of a tree, feed the homeless, then savagely beat minorities it is not a zero sum game. People in a position of power abusing their authority can jade entire communities against trusting them ever again.