I handle about 3 million dollars in auto insurance claims a year so I know where you're coming from. I challenge them daily. If you had a shop handling your claim they should be doing the leg work for you. It's up to the shop to negotiate the price, and if you have a good shop they then fix the car properly no.matter the agreed price. Also, don't agree to settle the claim until the car is finished. There is almost always supplemental damages that will need to be paid while the repair is on process. Don't cash out on the claim. This is how the minimize their severity.
Insurance companies don't order parts. They choose specific parts based on many factors mainly cost effectiveness. It's up the the repair facility to negotiate these prices and part types. And also remember used parts are usually no more used than the ones on your car.
Also to the original poster, if you need a repair estimate written I can assist you with it. I would just need to know the labor and material rates in your area.
