As I read it
"Depression and anxiety are, for the large majority of cases, emotional signals that one’s psychological health is not ideal and that one’s psychosocial/relational needs are not being met."
looks like a theory and and experimentally testable and falsifiable one at that. Take a bunch of depressed people, try to fix their relationship needs along the lines mentioned in the article, survey the people who now have friends, get on with their family and so on and see if they are still depressed and compare to a control group. Simples.