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.