So...your insurance is covering it? At a minimum, you need to at least get another quote. As far as I know, those are your rights. There's some guy around here, Trekken, I think, not sure, that knows all about that insurance crap.
Once, I took my wife's expedition to wal-mart for an oil change. The dumbasses backed her car into another vehicle, and messed up her bumper a little bit. I was put into contact with their insurance company. I got 2 estimates, and they cut me a check for the lowest estimate. They sent me a check for over a grand. I turned it into toy money, and never painted the rear bumper (which was barely noticeable).
Another time, I wrecked my sport bike. Got some estimates and sent them in. My insurance company at the time cut me a check. I ordered all the parts I needed off ebay, etc., and repaired the bike myself, so I pocketed labor costs, and saved money from what the motorcycle dealership wanted to charge me for the parts.
Not sure why your insurance company would DEMAND how you replace/repair it. If I were to be a skeptic, I would guess that the body shop guy would make more profit somehow, if you get him to order the OEM parts and repair it, rather than using your insurance check to order whatever the hell you want, and put it on yourself