Its a korean spa, it would be highly unusual for them to be clothed when doing any sort of bathing. They use big baths that are like shallow swimming pools, many people at once - kind of like how locker room showers are not private. Think giant naked hot-tub. Its sex segregated like a locker room for obvious reasons. But anyway, I digress, they don't want a bunch of americans wearing swim-suits like its a giant american hot tub - thus making them the weird ones for being naked in their own korean spa - so they require that people follow this rule to protect their traditional bathing experience