The healthcare services paid for by the government is (i) provided by profit-motivated companies with all the private sector incentives to overdiagnose and (ii) typically performed at lower rates than those paid by private insurers, and much lower rates than those paid by individuals without the relevant insurance cover.
Well plenty of health care providers refused to service Medicaid patients because the rates are so low. That would infer that they aren't getting what they want from the gov't.
