What if you are rear ended by a fault driver and his insurance denied liability?
If you have a police report from the incident, you can try to prove that it was the other guy's fault. However, if you simply exchanged insurance information, there's nothing stopping the other guy from changing his story, at which point it becomes a he said/she said argument, with the insurance companies trying to save their money. If you can't "prove" it was his fault, and you didn't involve the police at the time of the accident, you're kind of screwed. Take it as a very expensive lesson to always involve the authorities as an unbiased third party.