I had the very same situation a few years ago when my wife's car needed a complete front end. (Honda CR-V)
The insurance company allowed for a recycled front end (both fenders, bumper, grill, radiator, A/C condenser, hood, lights etc) and gave the bodyshop the OK to start the work.
When I saw the recycled front end that had been delivered to the bodyshop, I told them I would pay the difference for new Honda OE parts. He said NO WAY.
I told them to stop working on the car untill I settled with the Insurance Co.
I argued for 2 days and won the case.
The car was sent to a Honda dealer for repair and I paid the difference in cost of parts