Hope for the best, but plan for the worst. That's sort of my overall, generic advice for people who've been in a car wreck, is you're in a car wreck, somebody rear ends you, they say, "Oh, I'm so sorry. It's my fault, here's my insurance card. I'm going to take care of everything."
I hope that's how it goes. I hope you don't have any problem at all, and you never have to talk with an attorney, but you want to get a copy of that person's license. Just take a picture right then and there. You want to get a copy of their insurance card, right then and there. You still want to call the police and make sure that an accident report is filled out so that your version is recorded by somebody else, just in case.
If law enforcement won't take a report there, go down to the police station and make one of your own. Then, call your insurance company and tell them what happened. You want to hope for the best, that this person is really going to do what they've said, and that their insurance company is going to treat you fairly, but if they don't, you want to prepare for the worst and make sure that you have taken all the photographs of the damage, you've gotten witness information, you got a law enforcement report, and you've told your insurance company your version, just in case you have to fight about this later on.
If you think you need to talk to an attorney, you should. It can't ever hurt you to talk to an attorney. The first consultation's free. Protect yourself, just in case.