The story being released says something like "they were detained when a staff member was asked his relationship to the girl group and replied that they were his younger sisters." Now, the funny thing about this, is that I can totally see this happening. Linguistically, the staffer's choices would be a translation of hoobae - which would be something like "they are junior co-workers" or " yeo dongsaeng" which would be "younger sister" - which isn't necessarily a familial relationship so much as a social relationship - and presumably it was someone who was oppa/dongsaeng or unni/dongsaeng with these girls, so it just translates weirdly.

Now, normally for a Korean to visit the US as a tourist, they don't need a visa. However they aren't allowed to "work" in the US. They need entertainment visas. The story goes they were going to film a mv, then arguably they'd need a visa (although I'm sure 50%+ of the ones are done guerrilla style since they aren't really getting paid here)

So, let's say they are coming in as tourists with no visa, one guy of a group of people traveling with this group of girls, at least one of whom is a minor, gets asked "what is your relationship to these girls" and the answer is "my younger sister" when they are provably NOT family. Yeah....I can see how that would get you all yanked in for questioning.

And then I'm sure when it got cleared up they were a singing group, they ran into the question of whether they were going to perform, or work, and how they can't do that on a tourist visa.

Yeah, it was a cluster fuck on the part of the entertainment company. Not quite as bad as the time JYJ's company forgot to renew their O visas and they couldn't perform for pay and had to do free concerts, but still, quite a fuck up that probably started with a screwup in translation.