I looked up that hitch the OP has and I was mistaken. Though similar in appearance, it's not the one I've had experience with. It does have the side to side pivot. The head looks the same, but it has double pivots. I can certainly sympathize with that sinking feeling when the trailer pops out of the jaws and onto the pickup bed rails! It seems clear that the kingpin had to be pulled out of the jaws to deform them like that, providing, of course, that it had not been previously damaged but not seen. If it was properly latched, it does seem the tow company could have some liability. I hope insurance will cover all your loses and you're not too unconvinced by it all.
