>> [or there's a] third variable correlated with both income and crime. For example, higher IQ or greater conscientiousness
Or... the consequences of being prosecuted for crime are heavily weighted towards taking away things you have: freedom, luxury, wealth.
If you don't have any of those things, because you're poor, the relative consequences for getting caught decrease.
Consequently, there's less of a disincentive to avoid crime, especially if it offers you a way to get ahead.
Rich people have a lot that can be taken by the state in retaliation. Poor people, notsomuch.