They don't have to know it's Plato, and it doesn't depend on whether the rest of what he wrote is correct. Works for just about any case where someone thinks they've got a pat, simple definition of "justice" (often implicitly the case, if not explicitly) and have drawn some conclusions based on that. All it needs to demonstrate (and it does it rather successfully) is that simple "I've got the answer to this moral question!" solutions usually... aren't actually simple, and haven't solved much at all, once you start picking at them. They seem correct only as long as you avoid thinking about them too hard—and they don't fall apart in technical or fiddly ways, but in ways that make them clearly insufficient even to a layman or to someone who prefers to reject philosophy when it gets too up-its-own-ass. Most positions of this sort are just too bad and ill-considered to be interesting.