The NYT tells us that doctors are really upset that the government is trying to find out how easy it is for patients to get access to their services. The article interviews several doctors who expressed anger that the government plans to have testers call for appointments without identifying themselves as testers. The purpose is to determine how difficult it is for people with various types of insurance (e.g. Medicare and Medicaid) to get appointments.
This is a standard practice for researchers. In fact, it would be outrageous if the government were spending close to $1 trillion a year on various health insurance programs without knowing how effective they were in providing care.
While the NYT did interview some people connected with the government testing program, it should have interviewed some independent experts who could have reaped ridicule on the doctors. Of course no one forces the doctors to practice medicine in the United States. If they find the government too intrusive, as several complained, then they have the option to work in Canada, the United Kingdom or any other wealthy country and earn about half as much.