ok 2 comments here:
when a friend of mine backed into my car a few years ago i had to get estimates from 2 body shops. the insurance company wanted to make sure that i wasn't just picking the most expensive company, i guess. i really didn't pursue it farther than this as it was my friend's insurance company that was paying, and i figured 2 estimates was reasonable, especially since i told the guys at both shops i was shopping around for the best price. so i guess the rules definitely vary from region to region, no doubt from company to company.
if i were you i'd do the math before having your insurance pay. you'll save $2500 by going through your insurance. so, ask your insurance co how much more your insurance rates will be if you make the claim? i really have no idea, but if your rates are going to skyrocket, perhaps you may be better off after a few years by paying all that dough at once. but again, i'm not sure, you'll have to check; maybe they'll jack your rate up anyway just because you've had an at-fault accident???