Originally Posted by trader4

I mostly agree about your insurance company not raising your
rates for an accident where you were not at fault. In fact, I posted
similar here. But while I think most insurance companies would
not, I don't think you can absolutely rule out that some might.
It also could depend on your driving history. Clean record, no
claims in 10 years, is one thing. But if you had some tickets, had
other claims, then I could see them using the latest accident, even
though you were not at fault, to raise your rates. But I agree, that
with the facts given here, I'd put the claim into my insurance company.

I think you're wrong on saying that you can take it anywhere and
don't need more than one quote. There is no guarantee that the
other party's insurance company will fully pay any price for the repair.
If you choose to get it done for $5000 and they say it can be done
for $2500, there are other reputable shops that will do it at that
price, then the insurance company may only pay the $2500. You
could then sue the other party to try to collect the difference,
but having a few quotes so you know what's realistic, what position
you're in to negotiate upfront, etc I think isn't a bad idea.
Simplest thing I'd do is take the car to the body shop of my choice
and have the insurance adjuster go over there to check it out.
That way, the body shop guy can tell him, "look, that also needs
to be fixed, you can't just replace this one piece, etc". If that
results in a good number, you're done. If not, then I'd go get
other estimates and start arguing.