Is that proven? Is it intuitively clear? What makes us think that a mixed team of programmers is better than a homogeneous one? Maybe it is in some cases, and isn't in others.

Several studies have reproduced a correlation between diversity and organizational success. I don't know of such a study for programmers specifically. I also haven't seen proof of causality - do better organizations have diverse hiring practices, or vice versa? But I've never seen a study that said that lack of diversity was a good thing. So far the evidence weighs towards diversity being better for your organization, though I wouldn't call it "proven".

I think if you're making a claim like this, you should point people to the studies.

You're right and I would prefer to link. It comes up in The Economist from time to time. I can't find the links right now.