Auto Accident

Pretty much, it's out of your hands right now.

Did you go to YOUR insurance, though, or THEIR insurance provider?

Remember, ultimately, that it's the job of their provider to get out of paying you by ANY means possible. NEVER, ever talk with them directly. Call up YOUR insurance provider, give them the contact info, and let them deal with it.

Also, I'm not entirely an expert, but I think that since they already offered to pay for the damages, you're fine. I've never involved the cops in any accident I've been in (the damage was either never serious enough, in a parking lot where cops would refuse to go, or I was on the clock and didn't have time to wait for police), and when their insurance offered to pay, I walked out with a check equal to the cost of replacing the damaged parts.

I think, though, that you should do two things:

1) Call your insurance provider and ask them this same question. They're the experts, and they'll know what this'll do.

2) Take advantage of the bureaucracy and get the parts replaced/check written out ASAP.

Jam it back in, in the dark.