[Nyx]

You can bypass Police reports on Amazon by saying the police in your area said they won't deal with such a petty case...

That's if it's really a petty case though. They'll shoot you down if it's something valuable that they know the police would make a report on.

What value would you say qualifies as a "petty case"?

I'd say anything over ~$500 they wouldn't view as petty.