Although I'm not sure why you ask, I'll take a stab at it.
Unless I'm mistaken, whenever someone is injured in an auto accident, responsibility for payment falls upon the person(s) who caused the accident. Once their liability or ability to pay is exhausted, the injured person is on his own. Then, yes, if the injured person is covered by Medicare, it will pay, just like anyone else's own medical insurance would.
If you're saying this somehow lends credence to the auto-insurance-and-Obamacare analogy, please explain because I'm not seeing it.
I'm just trying to understand if state auto insurance, not for cars but for bodily injury, is a closed system. That is; is it entirely contained within a state. I think not.
It's logical for states to make you carry insurance to cover injury you may inflict on yourself or others.