The insurance company is required to pay the amount to fix the car or purchase a comparable replacement. They aren't required to provide a better car than what was lost. They will have data on the going rate. Calling Xist's Camry mechanically sound is a bit iffy and it certainly had cosmetic issues. You can find ads for a running Camry in the area in the $3,000 - to $4,000 range. Asking for 2 or 3 times that is nuts and just going to shut down any negotiations and move it to arbitration.
Clean 2006 Camry LE with 146K miles in Phoenix for $3000
https://phoenix.craigslist.org/cph/c...527449603.html
As to the claimant holding the cards - not so much. Generally the insurance company holds the final card which is binding arbitration. I ran into this when my wife's super rare 1987 SRX250 was damaged by the moving company on our move from Tennessee to Alabama. They started by offering blue book which was very low due to basically no data. I countered with the handful of listing and sales of similar bikes. We went back and forth for 3 months before the mover's insurance company laid done the trump card in a letter saying that they were done negotiating and the case would move to binding aribitration as dictated by the small print. Oh, and they get to choose the judge to be the arbitrator and the location. Please be in Chicago at xx time on yy date. We were a bit less than $1000 apart at that point.