Insurers have a significant incentive to get you to patronize their "preferred" collision repair shops. They keep vast amounts of money by effectively controlling repairs -- money and savings that are not passed on to you. This happens when the insurer demands a discount off of parts prices, urges the use of salvage yard parts or imitation crash parts, inhibits normal increases in rates charged for labor, and tells the repairers they cannot charge for certain normal repair activities. You still pay the same deductible you would pay at any shop. The insurer is the only one that benefits from your patronage of its "preferred" shop.
When you patronize one of the insurer's "network" shops, the shop has typically signed an agreement with the insurer that requires the shop to use salvage yard parts or imitation crash parts in the repair of your vehicle. Unbeknownst to you, this issue has already been decided for you by the arrangement between the insurer and repairer -- long before you ever had an accident. And insurers monitor their network shops to see if they are complying with the insurer's money-keeping demands. Shops that don't use enough salvage or imitation crash parts in their repairs in the insurer's opinion get negatively rated and are often kicked off of the insurer's program, no matter how good their repairs or customer satisfaction may be.
These insurer agreements with collision repair shops also require shops to fully indemnify the referring insurer. So, although the insurer is effectively telling the repairer how to fix your car, what parts to use, and what procedures and activities don't need to be done to properly repair your vehicle, the repairer has to follow the insurer dictates, take all the liability for the insurer's bad decisions, and pay all costs, expenses, attorney fees, and judgments someone might win for a bad or negligent repair. The repairer's garage insurance carrier is unlikely to accept liability for this agreement, so you could easily be left without a meaningful remedy if the insurer's network requirements for the shop shield it from responsibility for a bad repair.