Maybe I'm missing something, but I'm not sure I see much wrong about this scenario. I mean, things COULD have went differently (benefiting you), but unfortunately they did not.
First off, the person you rear ended didn't have to get the police and the insurance company involved, but chose to being that it wasn't her vehicle. Maybe if it was her car, she would have been cool about leaving those two out of the equation, but that wasn't the case. Honestly, if I were driving someone else's car, I might have done the same thing for legal purposes. If this accident had to go to court, a police report would probably be a huge factor in the case. Now IF it were MY truck (2002 Toyota Tacoma ) I might have let it go.... but, my truck has been rear ended four times (that I can remember) and I've never taken it to the shop to repair because the damage was minimal.... the cars that rear ended me, however, well they were pretty fucked up.
... sorry, back to the subject....
The second thing that (obviously) didn't go in your favor was the ticket. In my experience, cops don't NEED to issue a ticket, they CHOOSE to. Maybe he took your question wrong? Maybe he thought that you were "challenging" him or something? But anyways, he CHOSE to give to that ticket. Kind of a dick move... I mean, talk about kicking a guy when he's down, right?
I'd try to fight that ticket btw.
Lastly, I hope for your sake that she doesn't take her new Audi to the dealership, because that'll be a pretty penny. Good luck, homie.