Aw, come on … 
Natural Science: any of the sciences (such as physics, chemistry, or biology) that deal with matter, energy, and their interrelations and transformations or with objectively measurable phenomena. (Mirriam Webster, my bold)
You can’t objectively measure anything in psychology. Psychologists and medical researchers alike merely apply the scientific method to phenomena too complex to measure objectively and without bias. As you say:
I’m happy to accept that Medicine can’t be a natural science for the very same reason. Perish the thought, but could it be that psychologists fall into the very trap outlined in the article?
