Will comprehensive auto insurance cover a claim if a tow truck damages your car in transit?

I would say that the tow truck is liable for this claim. This is also what your insurance company will say even if they go ahead and pay the claim to keep you happy. Most of the time your company will pay then they will subrogate against the responsible party. If you have comp and collision then their is no issue. If you have comp and not collision then issue of what happened may come into play.