My bad, skipped a chain of thought there. Since medicare pays less than private insurance, hospitals can and do shift costs (which in reality is "opportunity cost of profit") to the latter, which pushes to private premiums up. Regardless, this is a minor effect. Very little of the inflation is justified with productivity gains, as you said it is a very inefficient healthcare system. US prices clock 2x-4x of comparable OPEC peers, admin percent is higher etc.