Well you could always request that they use OEM parts and ask to see the invoices for them.
When I had my doggy incident, I told Progrressive to have the car fixed at the David McDavid colission center across the street form the dealer I bought the car at. They complied and the part prices on the invoice were very close to dealer prices. The only thing that was not new was the bumper cover. It wasn't my old one but it was repainted.