I've seen speculation (though I don't currently have a source available) that "out of pocket" in that sense is intended to reflect that the subject is uncontrollable or not manageable. Which actually originally surprised me because it implies a connection between "out of pocket" (in the sense of unavailable) and "in the pocket" (as in, controlled by or heavily influenced by an outside entity; "that politician is in the pocket of Big Oil").

I also have this sneaking suspicion in the back of my mind that I've heard "out of pocket" used in a film, maybe by a spy or secret service agent referring to a VIP not being where they're supposed to be, but that's also something I don't have links about. It would fit in with the above concept, though.

So maybe the middle managers who use that shorthand are trying to sound like loose cannons and suave people of intrigue, when really they're just dropping off their dry cleaning or something similarly mundane? "You can't control me during this time, I'll be at my 7-year-old's ballet recital!"