Glad you made it back Ronnie.
Having been stranded myself by the side of the road 3 times [water pump pully, coil pack/ignition module, fuel pump] here is what I learned. Your towing insurance carrier is calling the cheapest places that they have a contract with and when they find one that will take the rate out they come. The proof is in the question they ask "Are you in a safe place"?
I no longer call the insurance company's towing service. I google tow companies near me and start calling tow companies. The guy comes out promptly, picks up your car, you pay by charge card and turn the bill in to your insurance agent to forward to the insurance company and they will pay. Never had a problem.
If it would have been an a crash the officer never asks you for your insurance card to call the towing service, he just calls the tow companies that police department deals with and out they come. The insurance company always pays them. This is no different other then there is no damage, but your car has to be off the road.