I'm not sure this is the case. Since medical insurance companies are heavily regulated on margins, their primary way of making money is investing the "pool" tha

I'm not sure this is the case. Since medical insurance companies are heavily regulated on margins, their primary way of making money is investing the "pool" that's used to pay out claims. The size of this pool is determined by actuaries, so it can't be increased arbitrarily. But it grows in two ways: more patients, or more required reserve per-patient. In this way, insurance companies actually benefit from higher hospital prices.