There's a comedic bit about that in one of those pulp thrillers. The President keeps trying to trip up the chef by requesting weird stuff, but the kitchen always comes through. But at the end of the book, the President sits down exhausted and just asks for a grilled American cheese sandwich—but they're out of American.
I'm sure that in reality, if they didn't have something, they'd send a runner to go pick it up real quick. Or nowadays, maybe doordash.
The U.S. Pizza Industrial Complex solution would be to constantly have a high number of pizza orders being fulfilled by various vendors across the tri state area, filling vast salt mine vaults with a strategic pizza reserve, thereby hiding the signal amongst the noise.