He could also name the NYT reporter.
The problem with people trying to shut down others primarily comes from individuals. Often that's individuals on social media. In this case it's a journalist. These individuals can destroy other people's lives, yet they essentially face zero consequences for doing so.
And each time they succeed, like in this case, they embolden others to do it.
Many of Scott's patients would find his writings to be very relevant information.
But, you say, surely that's not a problem for well-adjusted people! Guess what the hell a psychiatrist does.
If they do dox the person, though, their name will be on the article, and you'll be able to find it.
The point though, is that this hasn't actually happened yet. There is still a possibility that the reporter will back out, and not publish the name.
At which point, the author wins, and isn't doxed.
By not attacking the reporter, yet it still leaves open the possibility that everyone can back down.