Because they have the same name and she mentions them when you talk to her in her villa. They also look similar.
Caitlin from the Elite 4 is the Girl of the Battle Castle seeing as she knows Cynthia and let's her live in her Villa in Pokemon Black an White during the Spring time.....
Yes, she is from Battle Castle and the reason you couldnt battle her is because she was one of the elite 4 in the unova region.
