"Their insurance company looked at it...."???? 
That sound backwards, doesn't it??
-When I get in an accident,
I always go to my insurances' authorized repair shop, or agent first!The shop gets paid through the insurance company to fix it...if they find more, the insurance company pays more.
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Then your insurance company settles with their insurance company.
So, I'm not sure why the "other possible damage" would cost you. The answer may be, "don't accept their estimate". Get your own, through your own insurance company. You shouldn't have to pay a dime, including a rental car while it is in the shop!
