I can't read that paywalled article, but from the sounds of the abstract, no methodology is introduced to demonstrate causation. Any correlation that does not in turn show causation is spurious.
Do you have more info? Would be great if you explain how they do demonstrate causality. Not really sure why it is on me to refute a paywalled article that has no indication of being relevant. Please note that the OC who posted the link to the study (and to whom I was responding) specifically said "correlated".
There is compelling evidence crime is correlated with inequality.