Walmart and feeding the poor

Here's an excerpt of what a piece entitled Walmart is no savior: More small businesses = healthier people had to say:

Those whose focus is on the health of our communities and on the pernicious effects of obesity and diabetes say that Walmart’s unmatched ability to provide affordable access to healthy foods like fruits and vegetables, especially in areas that currently lack them, outweighs the potential negative effects the FWW report describes.

But a recent study published in the Cambridge Journal of Regions, Economy and Society suggests that communities that invite Walmart in may be making a devil’s bargain. The study found strong evidence that communities that rely on big box retailers — and large corporate employers in general — are less healthy and have higher rates of obesity and diabetes than those that don’t.

I'm wondering if they're controlling for all factors though. It would seem likely that communities oriented towards big-box retailers are less walkable. Downsize a Walmart, make it the size of a smallish business, and integrate into a walkable community and I wonder if you'd avoid at least a large portion of the effects noted.