A simple way to answer this is to call the Shelby County health dept. first thing Monday morning and ask them point blank.
It’s been a few years since I’ve been in Memphis, but I get to Nashville quite a lot and can tell you that mobile concession stands housing Mexican Taquerias are set up in parking lots everywhere you look around there. Drive around Memphis this weekend and see if you spot any of these. If you do find any, then I’d say you have your answer. If the health dept. refuses you a permit, but allows these Mexican vendors to operate, I’d say you’d have serious grounds for a descrimination suit with the city.