Authority would be where a doctor has the power to enforce their treatment.
This is a specialized use of the term. Authority can have many shades of meaning.
One of the things we face is confusion. There is a lack of knowledge early on, and our friends, family and doctors don't understand either (unless you are fortunate). Sometimes we have self doubt, peer pressure, and a list of doctors who have written us off. So when a doctor, armed with dangerous or false information, comes along and tells us he knows the issues, and has the treatment, we WANT to believe them. We are vulnerable and they seize power over us, though typically in their view of our best interests.
Authority also refers to citing of expertise or literature, or other authority figures, which is the behind much of bad medicine. Its why the evidence based movements are so powerful, in part. Doctors and other experts are often wrong.
Doctors often compound this by rejecting people who do not immediately follow their advice. "I am right, so if you reject my advice you are wrong." This mentality is a huge part of what is wrong in medicine, and is based on fallacy and power.