Earlier quoted context omitted.
Providers determine your rates. Insurers are companies providers recruit to collect their bills. In the entire US health care system, the providers are the only ones whose cash flows are capped by statute. A provider can charge whatever it wants; over 80% of an insurers cash flows have to go to the provider by statute. (The health care industry is a mess, I agree!)
You seem to be implying that the providers set the prices, but isn't it true that insurers can pick and choose which providers they cover, and because of the large amount of patients they insure, they have a huge amount of negotiation power to exert downward pressure on what providers charge?
Medicare is better than private insurers at regulating prices (to wit: when Anthem tried to adopt Medicare's rules for anesthesiology comp, they were excoriated, and the governor of New York proposed a statute preventing them from doing it). But they still wildly overpay for services; in fact, what they pay is not really materially different from what private insurers do (it's less, but not by that much).