If you look at the graph on page 8, you can see obvious clustering of poor countries vs other countries. This study does not compare the overall wealth of the countries against crime.

The reason that is important, is that in a rich country, even poor people have many options. In a poor country like Venezuela, they don't. As a result, even if they had the same Gini coefficient, the crime would look much different.

So when you take that into account (which is what I tried to do in my statement, but probably could have worded better), then being in a "rich but unequal" society is much better than a poor country of either high or low inequality. I think the high clustering of OECD countries demonstrates this.