There is a "grocery store" myth related to Detroit, and it is just that, a myth. There a numerous markets and stores in Midtown and Downtown that supply fresh food to residents.

Edit: I lived downtown for nearly a year and a number of grocery stores opened in the downtown business district while I lived there, with plans for more. According to this article [1] from 5 days ago, there are 80 grocery stores in Detroit. Not to mention the awesome Eastern Market year-round farmer's market.

[1] http://www.huffingtonpost.com/jay-walljasper/detroit-fresh-f...