Speaking as a tenured professor of clinical psychology, this part kind of irked me a bit. It's not exactly false but it's a little misleading (like some other parts of the essay).
Lots to say about it but this is a finding that has been reported intermittently for decades. However, it's being spun a little misleadingly.
Note that the author says that untrained professors were selected for their ability to be warm and empathetic. It's not everyone (we all know not everyone is warm and empathetic), and even trainees learn very very early (like immediately in their first term) the basics of therapy. Not everyone is warm and empathetic, and people going into clinical psychology are sort of self-selected in their empathy to start with.
This research is kind of being taken out of context too. Wampold, one of the authors cited (who I have the greatest respect for) is very big on "nonspecific factors", meaning things like empathy, good social skills, and so forth. His studies in general tend to be focused not on "does training matter?" but "do specific therapy protocols matter, or is it about the clinician's social/relationship skills?"
If you want some kind of medical standards, you can't just say "oh it's ok, everyone can just be warm and empathetic". You have to train on it, grade it, hold it to some standard. Otherwise you get manipulative, self-serving therapists who do harm in the long run (the length of a study versus real settings is another issue).
Another issue is that many of these issues are not unique to psychology. In lots of medical scenarios it's been shown that the amount of training needed to competently do a wide variety of procedures is lower than current standards in the US require. Experienced clinicians in many fields have acquired biases that interfere with practice, young trainees are much more worried about performance and are more open-minded and so forth (on average a little; not trying to stereotype).
A huge, enormous volume of studies over many years have shown that therapy works compared to all sorts of placebos and controls; that some therapists are reliably better than others; but that what makes therapy "work" overall is not what protocol-driven therapies (CBT etc) assert. It's not so much that training isn't necessary, it's that the field has has been obsessed with scientific details that, although well-intended, don't matter, and healthcare in general is full of phenomena that we'd rather not admit.