Too Dangerous to Play Outside

I guess I'll throw this out there for your general edification:

Children who live in neighborhoods that their parents believe are unsafe are more likely to be overweight than those in neighborhoods perceived as safe, according to a study in the January issue of Archives of Pediatrics & Adolescent Medicine.

Link.

My question: Are unsafe neighborhoods also the type of neighborhoods that have a disproportionate number of denizens on public assistance? Could the link to obesity, in reality, be the existence of a public assistance demographic, as opposed to the existence of a criminal one?