You may wish to read the statement below again:
59.1-207.4. Offer to return replaced parts required; customer's right to inspect parts.
An automobile repair facility shall offer at the time the repair work is authorized to return to the customer any parts which are removed from the motor vehicle and replaced during the process of repair; provided that any part which is required to be returned to a manufacturer or distributor under a warranty agreement, trade-in agreement or core charge agreement for a reconditioned part need not be returned to the customer. If the customer wishes the return of replaced parts subject to core charge or other trade-in agreements, customer agrees to pay the facility the additional core charge or other trade-in fee. The customer retains the right to inspect requested returned parts even if custody is refused.
A manufacturer or distributor of automotive parts can require the repair facility to return the original failed part to them as part of a warranty agreement, trade-in agreement or core charge agreement. This is a deal between the part maker or distributor and the repair facility independent of any agreement between car maker and the customer. As long as the part newly installed in the car can be considered a "reconditioned part" then the return is not required.
In this case, Tesla as the distributor of the repair parts can require the service center (also owned by Tesla) to return the parts to Tesla.
His car is not under warranty and he said there is no core charge. Therefore the provision you highlighted in red does not apply. The next line also states the customer has the right to pay the core charge and receive the part. It appears Tesla isn't even offering that as an option.