Consider that possibly the stated reason is not the true reason.

Maybe the authoritarian regime that run NK wants to control the way people look for various reasons: So the people don't culturally identify with other societies, so they don't spend time messing with more complicated styles (hair and other) because they consider it a waste of resources, so the people don't realize that the mere fact that outsiders can spend resources on more elaborate styles is a product of those societies being better off, that they want the people to internalize a shared society through uniformity, etc, etc, etc.

... and that in order to achieve those means, they will say anything regardless of truth, evidence, etc, and will punish dissent so that the truth doesn't matter (mostly).