To name but one example (of dozens), a study showing that countries with higher Gini coefficients are more prone to rioting, strikes and civil disorder, after accounting for income (third-world countries are obviously more prone than first-world) would qualify as proof of at least one part of the theory.
I agree with you 100% that the linked article sucks awfully.
Your proposed study, however, is so riddled with confounding factors that to call it a proof is nonsense. The man the article talks about does have lots of papers giving evidence for his views, and you should indeed read them if you're interested.
However, neither the study you propose nor any other study would constitute proof (of what? it's unclear what we're even discussing a proof of).
All I'm trying to say is, this is about human affairs, not physics, and we're not about to start finding proofs of human affairs.
