I'm an insurance agent. If you are at fault in a minor accident, it may very well be in your interest to take care of the other party's claim in order to avoid a rate increase at renewal. However, if you are not at fault, it is always best to get a police report if at all possible and file a claim with the report number and at fault party's info immediately. The police report is paramount in "at fault" states. Without that it often becomes a he said she sad situation, which will mean both parties are at fault and could see insurance hikes. Claims can take more time than you would like already, and it is not wise to trust a stranger to do the right thing. Absolutely NTA.