Oh, yeah, I'm sure that even with how secretive and "we are ancient conspiracy" the Veiled are, someone would recognize that headquarters is not the best place for a traumatized kid. A powerful ally's out of the way farm with other kids her age would be a great place to send her to recover.

Then someone had to explain to Nepeta to keep the play-screaming to a minimum while Karkat's weird friend is around because it gives her panic attacks.