You're precisely wrong, actually. The source I would quote is unfortunately a dead-tree book, specifically the first chapter of the book 'Nine Crazy Ideas In Science'. The first chapter isn't even ABOUT economic inequality, but actually about the 'crazy idea' that tons of guns in a society could lead to less violent crime. The only actually sensible thing to do, of course, is to study EVERY society and not to cherry pick 'oh we'll only look at the developed countries and then claim to have found something about human society in general'. You look at all of them. And when looking at all of them, prevalence of gun ownership in a society had no correlation with violent crime. Not positive, not negative. So they threw in a thousand+ other demographic factors and couldn't find a single one that was a statistically significant predictor... except economic inequality. Poverty itself wasn't predictive, wealth itself wasn't predictive, only a presence of both poverty and wealth together was predictive, with the extremity of the gap predictive of the severity of the violent crime.

One thing I am uncertian of is how exactly they defined 'violent crime'. Most people only consider street crime when addressing the issue. But most death from crime is due to white collar crime. White collar crime (at least in the US) kills more people and causes more economic damage than street crime by a large margin (but is socially normalized among the upper class so rarely punished, and then only lightly).

Correlation, we all know, does not equal causation. On guns and inequality. Doesn't matter if there is a statistical correlation or not. It proves nothing.

For certain societies, banning guns might lower crime. For others, it might increase it. There's lots of complex factors in any society that can influence whether certain economic or legal policies are taken.

For example, a country with a strong militaristic culture and a law for drafting all of its citizens to the army, might have lower crime despite the prevalence of legal gun owners. All sorts of possible reasons for this.

Likewise, an island nation with strong border protection could ban guns altogether and probably see a drop in murders. It's all possible.

Societies are complex and woven with history, traditions, sub-cultures, economics, politics, and natural inclinations that can all influence the outcome of any policy for better or worse.