I'm pretty sure if you are a known CIA agent you couldn't possibly be covert.
but but but but she was a super duper secret super spy!
So when we see these movies where the undercover CIA agent has this cover job as an insurance agent or whatever, that's not how it really works! The CIA's cover story is "You work for the CIA."
She was covert, and then went into CIA management in an noncovert position. But just because she made that shift doesn't mean that you can disclose that she was previously covert. The law protects the identity of previously covert operatives, as well. The purpose is to protect the CIA, and to protect her prior contacts, who were probably still covert.
But the key is that Rove did not disclose that she was covert. He talked to Cooper about her, but did not tell Cooper she was covert. In fact, he did not even know she was covert.