The policy decides the parts, not the shop
Most policies permit the use of aftermarket or recycled parts of like kind and quality. On an older vehicle that is reasonable and keeps premiums down. On a newer or higher-value car, owners frequently assume original manufacturer parts are guaranteed, and they usually are not unless the policy says so.
An OEM endorsement exists and is inexpensive
Several carriers offer an original equipment endorsement that requires manufacturer parts for repairs, often limited to vehicles under a certain age. For a recent vehicle it is a small premium for a materially different repair.
Safety systems raise the stakes
Where a part carries a sensor or forms part of a crash structure, fitment and calibration matter more than appearance. That is the practical argument for manufacturer parts on a modern car, rather than a preference about quality in the abstract.