You're not completely correct. Medicare has fixed prices that it will pay for visits, procedures etc. The prices depend on what region of the country you live in. Insurance companies then set their prices up or down from there. Independent physicians have little negotiating power and often get paid by private insurance companies less than the fixed government rate. Larger systems with more bargaining power can get significantly more.
But medicare's irrational price setting system is a big part of the problem.
It's the same thing, when it comes to the problem I'm pointing out, no matter how we describe it - medical providers charge different rates for the same products to different insurers, and insurers pay different rates for the same products to different providers. And the range of variation is not actually large, but we introduce tremendous complexity to the system in order to achieve it. It's not "competition" in the classical sense, and doesn't provide the benefits of competition to consumers, providers, or insurers.
