They're referring to liability insurance, which means their insurance will cover someone else's stuff if they damage someone else's car while driving your car. That has nothing to do with covering your car for damages. However, their insurance also covers your car while it is in their "care, custody, and control." If they damage it, or if the shop catches on fire, etc. their insurance will cover your car.

That said, if it were my car, I would also insure it myself. That way, if something does happen, and you don't like the way their insurance is handling things, you can turn it over to your own insurer. Lots of collector car companies offer coverage for projects/cars undergoing restoration. It's cheap, too.