No, doctors aren't lawyers. But they are humans, and thus they're responsible for their own actions, even if they've been misled by so-called experts. They bear responsibility for refusing medical treatment to clients who refuse to sign ridiculous "mutual privacy agreements".
I reasonably expect that highly educated doctors should have enough skepticism and worldliness to recognize that there exist people who will try to take advantage of them, much like "Medical Justice" has done here. Demanding that patients sign away their rights to public expression of their opinions is prima facie ridiculous and should trigger the bullshit meter of any doctor I'd consider trusting my treatment to. If doctors' bullshit meters don't trigger there, I shudder to think what pharmaceutical companies and free lunches could sneak by them.
Think about the constraints that doctors operate under. They're bound by doctor-patient confidentiality, and certainly aren't allowed to tell the whole world what they think of you. So they might well think it's reasonable that you're not allowed to tell the world what you think of them, either.
But if you say something nasty about them, I don't think they can even defend themselves because they cannot say anything about your health story, so it is a bit more complex than just running a business.
Saying that doctors are the only ones bound by privacy concerns is incorrect.
A lot of businesses cannot bad mouth customers or defend themselves in public due to how badly it looks to hash out all the details between the parties. If you check out WebHostingTalk.com you will see that sometimes hosting providers and dissatisfied customers will get into multiple page slugfests over who was in the wrong. This just makes the hosting company look unprofessional.
Let's say someone wrote a negative review about a cell phone store: "They wouldn't give me a cell phone! They're a horrible company!". The cell phone store isn't going to reply back(in a public space) "You couldn't get a cell phone because your credit was terrible & when we ran your card for a deposit it came back as declined!". It makes them look bad for airing the customers dirty laundry in public. A generic response & a request for the customer to contact them on the issue is the best they can do in that situation.
These review websites sometime have a feature where the business can become "verified" which allows them to respond back to these posts with at least something generic like "Dr. X has attempted to communicate with Customer Y" or something generic like "I am sorry to hear of your problems, please contact us @ xxx-xxx-xxxx so we can help resolve this matter". This is probably the most any business can do as far as communicating details about a certain customer without looking bad.
I reasonably expect that highly educated doctors should have enough skepticism and worldliness to recognize that there exist people who will try to take advantage of them, much like "Medical Justice" has done here. Demanding that patients sign away their rights to public expression of their opinions is prima facie ridiculous and should trigger the bullshit meter of any doctor I'd consider trusting my treatment to. If doctors' bullshit meters don't trigger there, I shudder to think what pharmaceutical companies and free lunches could sneak by them.