can an auto insurance company prove it was my fault

What is the name of your state (only U.S. law)? nevada

I was involved in a small fender bender accident and there was no police involved, no pictures taken, no witnesses, and no evidence. Both parties decided to exchange name and number to settle it. The person called the next day stating he wanted 5,000 for damages. Next day their insurance called and stated their client made a claim and they wanted to take pictures of my car and said it was my fault. Because there is no evidence, no proof and only he said she said can I tell the insurance I do not know what you’re talking about and that I never got into an accident and to show me proof or leave me alone? My car had a little scratch on it and theirs was already in bad shape. I was told since there is no evidence to not even say I was involved in an accident or they will find a way to prove it was my fault threw my own words and since the scratch is in the front of my car and the back of theirs they will pin it on me. So can I say I don’t know what you’re talking about I never got into an accident and show me the proof or leave me alone? Thanks for the help.What is the name of your state (only U.S. law)?

Doesn't sound like you have much of a defense at all. How would they have gotten your information if you weren't involved in the accident? Report it to your insurance company, TELL THE TRUTH and let them handle it.

Re:

Even if they only have my name and number and no insurance info. They also gave no info other then their name and number? Thanks for the help.

Sounds like they can identify you. That's enough. Why would you lie?

Hi, to be honest, the guy who was involved in the event was acting very weird and my wife was scared. He said he did not want to get the police involved and since there was a little scratch my wife said ok. When the guy called me 2 hours later saying he wanted 5,000 for the damage that day or he would put a claim with his insurance, I stated that it was not even my wife’s fault and you did not have 5,000 worth of damage. After talking to a few people they said unless there is proof via police report, witnesses, and pictures, insurance info, admission of guilt, there is nothing to go by besides he said she said. Something tells me this guy is a pro at this cause his insurance was not on site at the time, that’s why my wife did not give hers. Do they have grounds to collect from me with no evidence? Thanks again for your help.

The evidence is the damage to your car and his car, and his ID of you and your wife and your vehicle.

Report the accident to your insurance company. If you are liable for damage, they will pay. They will pay for the damage you actually caused, not for some money the guy would like to have.