You’re right, they’re deluded.There are produce stores and bodegas on nearly every corner in upper Manhattan, even in Harlem. You can see it in Obama’s autobiographies - he’s ashamed of his origins, and tries to imagine an alternative life story that better suits his own vanity and sense of self-importance.
I can walk from Eli’s bread factory all they way down to WTC and hit grocery stores every other block, convenience stores and well fruit stands in Washington park and other parks.