In the past 10 years or so, the notion that unhealthy eating and food deserts are related has been refuted in multiple articles and studies. Here are links to some of the more popular ones.

[1] NPR "The Myth of the Food Desert": http://www.npr.org/2010/12/15/132076786/the-root-the-myth-of...

[2] New York Times "Pairing of Food Deserts and Obesity Challenged in Studies": http://www.nytimes.com/2012/04/18/health/research/pairing-of...

[3] The Atlantic "Do Food Deserts Cause Poor Eating?": https://www.theatlantic.com/business/archive/2015/11/food-de...