I agree, the other guy ins't involved from your perspective. However, if you contracted with the hauler, I'd think he's on the hook regardless of what or who he subed out too. I'm sure he can't operate without being bonded and or insured.
As long as you can tie you and the transport company together. Forget the driver, it's the transport companies respionsibilty if you contracted with him.
Just a guess though. Hope it works out. If not, what about your insurance? It should cover unless your policy has a clause like so many do, that it's not covered when someone else is towing it outside of X miles. I think my old policy said over 250 miles from "home" (where it's insured from) and it was mine if someone else was towing.