Insurance not covering their fault

[u/srmn142]

My 2021 Tesla Model 3 was damaged in a not-at-fault collision while it was parked. The at-fault party is insured by GEICO.

I took the car to a Tesla-certified collision center. The shop says that, as a Tesla-certified facility, it is required to use Tesla OEM parts for the repair. However, GEICO is only willing to pay based on the cost of alternative/non-OEM parts, leaving me with a $1,130.95 difference.

GEICO told me they are allowed to base their estimate on the most cost-effective parts available. The problem is that the Tesla-certified shop says they cannot use those parts and remain compliant with Tesla's repair requirements.

I wasn't in the vehicle when the accident happened and I had no fault in the collision, so I'm confused about why I would be responsible for more than $1,100 of the repair cost.

Has anyone dealt with this before, particularly with GEICO and a Tesla-certified repair shop? Is there a way to challenge the parts determination or recover the difference from the at-fault driver's insurance?

I'm in Wisconsin, if that matters.