Medicare Advantage Plans look like private insurance, but they act a lot like regular Medicare when reimbursement gets involved.
What happens when Medicare has a right of reimbursement that competes with other types of liens? Well, let's say that most of the time, it isn't pretty for the other guys.
It's important to audit Medicare's asserted right to reimbursement. They won't do it for you, and if the Program gets paid for unrelated treatment, that money's going to come straight out of your pocket.