Does the towing company's commercial insurance cover a customer's vehicle if it is on the bed of the tow truck and an accident occurs that is the tow driver's fault?

normally yes if your car is damaged as a result of the accident while the tow companies driver is operating the tow truck, and your car was not damaged prior to the tow company picking up your vehicle ( for example your car broke down on the road due to a mechanical problem , or if your car was in a collision prior to the mishap with the towing companies driver ,the towing company would have to pay for any additional damage done to your car beyond what was damaged in your original collision- unless you had pictures it might be hard to prove that ) A good thing to do is to mark the paper work for the tow company that there is no damage to your vehicle or note the damage prior to being towed , this will eliminate the problem you have now. If the tow company does not want to submit your claim, immediately contact an attorney and go after them vigorously or they will ignore you and you will get ripped off in full