Jack, you didn't read it with a critical eye. Why? Pick a city. ANY city. Then Google it, dig around, and find out which neighborhoods have the highest rates of crime within that city. Yeah, you do know what you'll find, don't you?
Where the study you referenced went wrong was that it stated that the crime rates were going down during the recession, and used that to claim that there's no positive correlation between poverty and crime. The great, glaring error is that your study apparently forgot that the decrease in crime didn't begin during the recession, but has been going on for the past couple decades. The decrease in crime continued nationwide - with exceptions within the margin of error, of course - even during the recession, which shows that there's other factors at play...
...but regardless of what factors may be at play, almost without exception, the most dangerous part of any city is going to be the poorest part of that city. You know this. You just don't want to admit it.