Calling the cops is a good idea!
My wife's mother (my mother in law?) had a similar experience in South Georgia.
She was rear ended by a couple. It was a simple fender bender and there wasn't much if any damage to either car. Still, after inspecting the damage, she insisted on exchanging insurance information -- just in case.
Immediately, the couple who rear-ended her unleashed a torrent of threats, slurs, and other obscenities. She felt threatened enough to get back in her car and call 911. They verbally assailed her from the other side of her window until they realized she was calling the police.
Eventually an officer arrives and it turned out he's good friends with the rear-enders. IMHO, the people who rear-ended her at least deserved an assault charge but nothing ever came of it.
Since then, I've decided that, for the reason jhollow mentioned, the first thing to do in a fender bender it to call 911. That way everything will be recorded and hopefully this will keep everyone polite.