What if the other driver lies about the accident? Please help!

What is the name of your state? Texas.

I was rear-ended a month ago on a highway. It was a raining day. The teenager driver admitted his fault at the scene. A patrol police car stopped by, but the officers suggested us NOT to file a police report because the damage was minor and liability was obvious.

I called his insurance company on the same day. Two weeks later they called back and denied my claim (damage < $500). They said the teenager driver told them that I backed into his car. Although they admitted that it would be unusual that someone backs on a highway, but it was still possible.

Without a police report or witness, what is my option now? I do not have collision coverage so my insurance compnay will not fight for me. Can I sue him on small claim court without any hard evidence? Thank you!

Lies about getting rear-ended

State=Washington

Have you found out anything about this?
I'm in a similar situation. Except that I have a witness. I was parallel parking and a woman hit me, and imediately claimed to the police that I backed into her even though I wasn't even moving. I wonder if this is a common thing to do. But like I said, I have a witness, and she saw me not moving. So what I'm wondering now is if she can get into trouble for lying to the police and delaying the investigation, making a false insurance claim, etc. How can I make sure she gets into trouble?