When I lived in NYC I always found this to be a lazy cliché - my grocery bills stayed about the same when I shopped there and the fruit and produce lasted much longer than cheaper stuff from the corner supermarket. Their own brand stuff is reasonably priced.
Now that I’ve moved to the country and shop in a “normal” supermarket if anything my grocery bills have increased, plus now I have gas to add to the total.
YMMV - my diet is mostly organic and 100% vegetarian
