No, that's not true. All the market power is with the providers, which is why they're responsible for something like 9x total health care spend in the US than all health insurers combined.
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).
