If you get into a car incident where there is no proof of what occurred, what actions can the person take...?

Small accident with only a few scratches on one car. No pictures taken. No police report. No witnesses. Insurances and registration exchanged by both parties. What can the person with the small scratches who's not at fault do? They can call the insurances, and tell them what happened, but what can they do without any proof? What if the other person denies the claims?