Here are some more details - I was not present when the car was towed. The apartment doorman is sure that he has never seen a flatbed used in that lot, but he's not willing to put it in writting. Subaru has stated that the damage is due to improper towing. The towing company said they used a flat bed, which I could see on my reciept, so I showed them my receipt, and it (surprise, surprise) didn't note that they used a flat bed.
I have also on the receipt the name of the tow-truck driver. I'm guessing the tow truck company will (or has) create a record showing they used a flatbed, so I will need to find a way to prove they didn't. That's why it would be helpful to know more about tow truck drivers and if they drive one specific truck or what... otherwise I am trying to prove from the damage that they couldn't have used a flat bed and they will probably just create a record saying they did.