It sounds like you've already gotten an offer for way more than the car was worth. To offer to reimburse you for any amount related to previous maintenance expenses is pretty generous. Take the money and run. If you feel it isn't fair, there is a way to avoid this hbuttle in the future. If you feel your car is worth more than fair market value, have it professionally appraised, and then insure it for the appraised value, if the appraised value really is significantly more than fair market. Let's say most similar cars would be $3000, but yours appraises for $6000 . . . insure it with your insurance company for $6000. If it is later rear-ended and "totalled", file a claim with your insurance company for the $6000 appraised value for which you have suffered an insured loss. Then your insurance company will probably go after the other insurance company for $6000. In the meantime, you have the money that is owed to you.
But unless you do have your car appraised and insure it for it's actual value, you shouldn't expect an insurance company to automatically pay you more than your car is KNOWN to be worth. -Dave