Shops become "preferred" by entering an agreement to automatically accept the insurance-determined labor rate (that may or may not match the market rate!) for claims work, with the "upside" that because they are preferred shop, there is a "steady stream" of customers who come to the shop as insurance claimants.
If a claimant gets insurance approval for the shop's rate ahead of time, it can work out with no concerns about who's paying. If the claimant picks a non-preferred shop and authorizes them to do teardown/repairs WITHOUT insurance approval? Problems may be incoming. It absolutely depends on the shop you go to.
If the claimant picks a non-preferred shop and authorizes them to do teardown/repairs WITH insurance approval, it will work out with no concerns about who's paying.