I haven't done auto since dinosaurs roamed the earth, and only NY, so take this with a grain of salt.
There is a lot on that list that Medicare won't pay. For example pain and suffering. Moreover, doesn't the insurance for the (medical) under the auto policy kick-in first, i.e. primary to Medicare? (If Medicare isn't paying the bill in the first place, they don't get paid back for it.)
Secondly, (and again, my knowledge is limited) say you are badly injured, and the party who causes the accident has a wopping 15k in BI limits or (State requirements differ), flees the scene or is uninsured.
Your attorney settles with the carrier for the tort feasor for their policy limits and then (again this is NY) submits a demand for arbitration for the policy limits of your Under Insured Policy. That may result in a settlement with your carrier; or it may go to Arbitration.
But - like life insurance - better if you never need it.
But - this is kinda like life insurance - better if you never need it.
Can Medicare get involved, yes, although typically their liens are much smaller than you might expect and are negotiable by your attorney. (Yes, you most likely would want an attorney to deal with this so you don't make any missteps which could either cost you access to your policy or fail to iron out any Medicare issues; such as whether or not a Medicare set aside is necessary.