Did anyone contact the police at the scene? If neither you or the other person called the police, you might want to check with your local dispatcher, a bystander may have called it in. I was in an accident once and it took over 30 min for the police to show up and we called them 3 times while we were waiting! And it was in a small town and no other accidents happened that day! If someone happened to call it in and said it was the other person's fault you could get your witness.
I work in insurance and if you have a good company they will do all this work for you. I would suggest going to your agent and reporting the claim, because if she has already reported to her company then they are going to be calling your company. It's better if they hear the story from you 1st then you just comming in saying they lied. If there isn't enough damage to bother fixing then they can just close without payment and it will not affect your record, it will just make it so she can't go out and damage her car more then blame it on you and you end up paying more in the long run. Now keep in consideration this is the way it is in Iowa and insurance rules are different in every state so contact your agent and ask them how long you have to report a claim and what the rules are.