Technically, if there was a clear sign saying that the private parking was patrolled and cars parked illegally would be towed at the owner's expense, then the owner can't blame the towing company. On the other hand, they can still be on the hook for acting stupidly, which seems to be the case here: It should be easy to argue that towing companies should know which cars are front - rear or all wheel drive, or be able to look it up easily on the internet. Having determined it was a rear wheel drive, use dolly or tow it the other way around.
