On average if having more money doesn't sate one's appetite for criminal behavior, and living in a better neighborhood doesn't either, then what variable is left?

The only reason blacks commit more crime than whites at comparable income levels is because even relatively better off blacks live in worse neighborhoods

This statement negates itself and simply shows that the primary variable of the problem is blacks.

Wealthier white in any neighborhood = Lower relative crime

Poor white in poor neighborhood = Lower relative crime

Poor black in poor neighborhood = Higher relative crime

Wealthier black in any neighborhood = Higher relative crime

It's nonsensical to write-off lower income whites as living in better (per capita income) neighbourhoods, despite supposedly being as poor as they are. On average, people live in as nice an area as they can afford.

The really funny thing is that it somehow shifts the burden on to the poor neighborhood instead of the person committing the crime.

It also assumes that most higher income blacks must live in these worse neighborhoods on average instead of leaving them, which again is nonsensical.

I have no doubt that poverty increases the probability of criminal behavior, but the trend is quite clear regarding the consistent pattern of criminality and one of the driving forces behind it. To simply say that it is non-zero despite the relative differences is not a suitable null hypothesis to start from. Differences exist, therefore a difference in outcome measures should result.