Yup, it's rear-wheel drive and a manual transmission. I think the damage issue is that the T-bar of the towing mechanism is rubbing up against sensitive bits on the underside of the car, particularly the front suspension. I'll know more when I hear back from my dealership.

(And, yes, I had a certain apprehension about "24", although this particular truck driver didn't really seem to be much of a threat. When I said to pull over and unhook my car, he did it without giving me any trouble. He only started saying stuff that I didn't buy when it pertained to his potential liability for damaging my car.)