Does Wealth Inhibit Criminal Behavior? Lottery Winners and Their Children [pdf]

Not denying what you're saying, but the abstract actually says "There is a well-established negative gradient between economic status and crime".

Just for argument's sake, one could propose that since lottery wealth is sudden and quite large, it has different effects than what is almost always a gradual rise in economic status. Or one could argue that un-earned (randomly awarded) wealth is different than earned wealth.