Does the "premises liability law" include accidents caused by being on someone eles's automobile? Or is there a premises law equivalent for autos?

Anything is possible, but that's why you have (or I hope you have) liability insurance.

There are dozens of circumstances under which a lawyer for the guy with the broken neck could argue you should be liable. Among the possibilities are a story that you asked him to go on the truck, you didn't tell him not to, you didn't try to stop him, he was reasonably trying to help you, the truck was inherently unsafe, there was an oil spill or other defect on the truck you didn't warn him about, etc.

That doesn't mean I'd throw in the towel. You and your lawyer would have also have all sorts of defenses to liability.

It all depends not only on the facts and circumstances that actually occurred, but more importantly  on what the trier of the fact (usually a jury or judge) believes occurred.