If the Repair Shop is a licensed business, they can elect to become self insured, but they would need a certificate or bond of insurance, to show that they could cover liabilities, up to a state required minimum, while any employees, were driving vehicles for business purposes. If they are not self insured then they would need a basic commercial or business auto liability policy to cover this. You can also elect to provide Workers Comp insurance for your employees.
I have seen shops that require customers to sign customized waivers so that the garage is not responsible for the vehicle while it is in their care, so you have to look into that to see what limitations or advantages it presents. Otherwise, the shop can become legally and financially responsible due to any issues that arise from operating the garage. For example the negligent repair of a customers car, which could lead to an accident or additional damages, injury, death, etc. There are other incidents that can occur to the shop directly which could result in damages to the building, equipment etc.
Garage Insurance insurance provides Coverage for bodily injury, property damage or destruction, for which the insured garage and/or its representatives become legally liable resulting from the operation of the garage. Repair shops can face the possibility of a liability suit for three types of damages: special, general, and punitive.
Special Damages are the amount of the actual cost of the persons expenses or out of pocket costs for the repair or replacement of damaged property, lost earnings, etc., General Damages are the amount for physical or emotional pain and suffering, loss of companionship, disfigurement, loss of reputation, loss or impairment of mental or physical capacity, loss of enjoyment of life, etc. and Punitive Damages are monetary damages that can be awarded to punish or deter you from similar courses of action in the future.
My point of explaining all of that is that if the Repair Shop (or owner) does not want to pay out of pocket for any loss or go out of business if they are unable to afford the financial burden of the loss, it's probably a good idea to have insurance. Nothing I stated is mandatory except the standard auto liability coverage that is required for any owned vehicle. I mentioned that initially as most repair shops or their owners have vehicles that are business owned or privately owned and used for the business to make parts runs, pick up customers, etc.
Auto Repair Shop insurance can be tailored with various types of policies to meet the needs of your business operation, your property and it's contents. The whole insurance question can get complicated, but hopefully I have shed a little light. If not I'm sure that you could contact several local agents or companies online for more direct info.
Good Question. Thanks for asking. ~J~