I have health insurance, so treatment for my bodily injuries is covered. Someone else is driving, so if his negligence results in a wreck I generally won't be liable to the other driver. I won't be responsible for fixing his vehicle.

That covers most garden-variety car wrecks, so there is little need to be concerned about my friend's insurance. I suppose if I were really on top of things, I would ask my friends for proof of insurance anyway, because maybe I would want to sue him for pain and suffering, which his insurance might pay for (my health insurance would not pay for that, or for lost wages.)

Never seen "riding around in someone else's underinsured car" insurance. Typical umbrella policy wouldn't cover that unless I'm negligent. I suppose I could get disability coverage which might help protect against the lost wages from getting injured in someone else's car.