There isn't any such causation between rich and poor countries. Most of Asia is dirt poor, even more so a couple of decades ago, yet crime is extremely scarce.

Even in America alone there are a vast number of people living in extreme poverty. And the overwhelming majority will live perfectly normal lives, even if it means on occasion living off iceberg and ramen, as was the case for myself when growing up.

If poverty/desperation drove crime then there would be vastly more criminals, especially in rural areas, yet criminality remains relatively rare.

You'll find far less tolerance for criminal behavior among those who grew up in poverty, because they are the ones who have lived through it all and seen with their own eyes the sort of people who go down the wrong road. And the fault for going down that road lies with nobody besides those people.