That’s absolutely not true, and the absence of clinical autonomy under private insurance is absolutely horrifying and completely indefensible. I wrote about it here a while back and I suggest you have a look. The intrusion of insurance bureaucrats into the doctor-patient relationship is absolutely rampant throughout the US health care system and would be considered intolerable by doctors anywhere else.
Here is a brief quote from a paper by health care economist Uwe Reinhardt (emphasis mine):
It is Reinhardt’s assertion that the absence in the United States of an overall program of budgetary control over medical expenditures, as is characteristic of the prominent European systems, results in unparalleled micro-management at the clinical level to achieve cost control unattainable on a larger scale. He writes that “…if the bureaucrats cannot somehow impose upon the healers an overall budget constraint ex ante, then they will sooner or later be driven to control their outlays on an ongoing basis, by monitoring each and every transaction for which they pay – that is, by second guessing both the providers’ clinical and pricing decisions” (Reinhardt, 1988). This appropriation of the clinical dimension of autonomy would be regarded as intolerable by physicians in other medical care systems. He suggests that “European and Canadian physicians would be appalled at the numerous intrusions into clinical decisions now routinely made by these external monitors in the United States. They probably would rise up in arms over that loss in clinical autonomy” (Reinhardt, 1988).
https://www.cms.gov/Research-Statistics-Data-and-Systems/Research/HealthCareFinancingReview/Downloads/CMS1191473dl.pdf