another student backed into our parked car

COLORADO:
Six days ago, another student backed into my daughter's parked car at a friend's house. Lots of witnesses. The student was a friend of the registered driver. She became hysterical begging not to involve police/insurance, called her parents and said they would pay for it out of pocket. We never spoke to the parents ourselves but went to get an estimate after the weekend, at which time the family then said not their problem since it wasn't their car (CO is a no fault state). I called my insurance who backed this up. IF we file insurance, our insurance will go after the vehicle owner not driver.
Is there a way to make the person responsible for the damage pay? Everyone's upset - these are all teenage drivers so imagine insurance... I am wondering if I pay for it myself, can I sue the family who is morally responsible? Or will I be told I'm going after the wrong people?
FYI - I filed a police report today and yes, I know I was stupid to allow the girl's tears to influence me.

Q: Is there a way to make the person responsible for the damage pay?

A: Sue the driver and/or owners. Having a judgment against you for a car wreck in most states can screw up your driver's license really bad...a great incentive on getting the judgment paid.



(I am saving your post to show my proposition: Always call the cops when there is a wreck.)

Find out the insurance that covers the car, and file a claim with them. It's not the parents' fault the kid hit your car, it's her fault. No fault does not apply to property damage in all states except Michigan. The insurance comes from the vehicle owner, not the driver, but the driver is the one who will get the black mark on her driving/insurance record for causing an accident.