Most of the area of food deserts (as defined by the USDA) is rural. People live out in the country (often by choice) and then show up in statistics saying that there are lots of people that have low access to food.
Poor areas in cities will often not have an immediate, large, well stocked grocery store, but they are probably only a mile or two away from one, and there will certainly be smaller stores with some fresh items.
Its almost as if not every capitalist country has horrendously idiotic city planning.