It would be ok to replace "Mr Smith tells me he has chronic back pain" with "Mr Smith has chronic back pain", if the former is enough evidence to make that diagnosis. If he was diagnosing Mr Smith with cancer, or depression, the doctor's note wouldn't include a scan of the tumour or a transcript of the interview: the doctor should abstract those away and just present the conclusion.
True, but the presumption in the case of cancer is that:
a) The doctor in question is qualified to diagnose cancer.
b) The doctor has made that diagnosis, in the medical sense.
In this case, Scott is a psychiatrist, who is unqualified to diagnose back pain or recommend any course of treatment on the matter. He believes his client when they say that they are in pain, but that belief is a personal, not professional, opinion.
He's a medical doctor. He's qualified to diagnose back pain and recommend (professionally, not just personally) the patient tries using his own chair. As I understand it the AMA would be OK with this, while they wouldn't be OK with, say, me (not a medical professional) writing the same letter and presenting it as a professional diagnosis.
He knows the limits of his abilities and wouldn't recommend the patient take 2 weeks off work, undergo back surgery or prescribe opiates. If any of those were in the discussion, he'd tell his patient he really does need to see a specialist.
I think that the point is that it isn't enough evidence to make a diagnosis. The article expands on why it is inappropriate for a psychiatrist to make a recommendation related to back pain. He's not just "the doctor", he's a specialist with a license to practice a limited set of medicine.
What should a psychiatrist write on a doctor's note if his patient claims to suffer from cancer, no other evidence given than the claim itself? Now, depression, that's something a psychiatrist can legitimately diagnose.
Because the main symptom of back pain is the patient reporting "My back hurts". If the patient instead reported "I have this lump in my testicles that wasn't there last week", I'd certainly think it's likely he might have cancer, and some good medical advice would be "go and ask a GP about that".
Back pain is a symptom in itself. Maybe a disk has been shifted, or it's caused by a kidney infection. Maybe it's just muscle pain or sciatica related. Hell, for all we know, the back pain is caused by the chair in question. Without proper examination you can't rule these things out and make a professional recommendation as to what to do about it other than "go see an expert or general practitioner".
By phrasing the recommendation the way he did he made sure that it is understood that a) he is treating the patient for an unrelated issue, b) he isn't in a position to diagnose back related problems and c) he never examined the patient's back problems.
This is especially true for pain diagnosis which is inherently subjective and if possible relies on self evaluation (even though some methods exist to complement or replace self evaluation with external observation).