Or make sure you have health insurance.
Your own health insurance is one thing - compared to it, your liability in the event of an accident is essentially unbounded.
How? I am not driving the car.
Yeah. Perhaps my comment was not clear. They made it sound like you were in grave danger if you merely rode in the car of someone with insufficient automotive insurance, to which my answer is "make sure you have health insurance." Actually, that's my answer to many things.
If you're signing up to do this as a rider, well I don't think you should given the insurance problems and you not having any guarantee that someone will be held liable if they cause an accident.
Getting into a bad accident with an underinsured driver at fault is a life changing event.