Wrong, no insurance company is legally liable to buy a car. They only owe the actual cash value of the car. That is an objective valuation.
If you re-read my post, you will see that I was trying to draw the distiction between whether this was an insurance settlement proposed by the insurance company of someone else, who was responsible for the accident, or was it her insurance company. If the former, she can get anytbing the traffic will bear if it was the other persons fault. She could get all sorts of related costs and inconvienience in a claim, and if they didn't want to settle for that tell them, "buy this car with this particular stock number on this car lot."
Certainly, if it is her carrier, the cash value, which the carrier is liable for under the terms of the policy, and the replacement cost (with related loan balance) aren't always near close enough for most people to come out well. But you don't have to be confined to those limits if someone else was at fault.