Is this claim dodgy?

Hi, I had a bump yesterday and bumped into the back of another car who had slammed on. The driver and front passenger got out and gave me a name and a number. They discussed whos name they were giving but I don't know who they were? There were some green L plates on but one of the girls said this is what happens when you drive and you wanted to learn, meaning that the girl didn't have a full license as she was clearly still learning. Will she have insurance? As they want to claim for whiplash, but she wont give me her details when I rang her up. At the time she 100% didn't want to go through her insurance, so I said that I would pay for the damage if she wanted, which I wasn't bothered about as it would save me losing my NCB anyway. What shall I do, as I think they are going to say that the owner of the car was driving, instead of the girl who was learning? I was in shock at the time and just took her name and number and the type of car, but not the registration? I know thats stupid but I panicked, please let me know what you think.

Also their brake lights weren't working, I'm not sure if that makes a difference? There were a police car there and they came over but they didn't ask for our licence or anything, they just asked if we were swapping details? Im not sure if they would be able to do anything as they probably wont have took notice which were driving and which were the passenger?

They also rang me today to say that they were going to claim against the police for whiplash (as the police car slammed on suddenly, making them slam on and me slam on, but I hit them just) and would I write a letter with them to state what happened?? Just sounds a bit weird to me? Why wouldnt they just claim against me, is it because they can then lie and say they that it was someone else who were driving? I dont know, but I dont think the claim against the police car would get far?