The conclusion he comes to is irrelevant. If others shouldn't be making a diagnosis without ever having met and interviewed Trump, then neither should he - regardless of the conclusion he comes to.
I get your point but I think you are wrong. It is unprofessional to conclude that someone is mentally ill on the basis of public statements and actions, but illness can be properly ruled out on the same basis. If Trump is seen not doing something that is necessary to make the diagnosis, then you can safely say he doesn't fit that particular profile. It is like technical fault-finding. Only one thing causes the problem, but many things can be ruled out.
Wrong, psychological conditions are complex a diagnosis cannot be made watching TV or reading press releases. I had a long discussion with my son( a Psychologist) about this and he agrees. These golf making these diagnoses are grand standing. A diagnosis is done over several in depth sessions with the individual over a period of time with followup review to confirm etc.