It's likely that we don't have enough details. If you get a loaner and sign a car rental agreement, then the responsibility is stated in the agreement. Some repair shops, though, just hand you a set of keys and loan the car as a fovour. That is not much different than borrowing a car from your neighbour, as there is no written agreement. In those instances, the insurance is on the vehicle, not the driver, and it is the car owner's responsibility to lend it to a qualified individual and accept the risks. So unless the repair shop has a signed agreement for loaning the vehicle, I think the insurance liability would lie with the owner of the vehicle, which is not related to the moral responsibility implied by the first post.