Are you mocking the idea of one single person being undercover by calling it a 'conspiracy'?
At best the FBI decided it was more important to catch these people than it was to prevent the leaking of some cc's.
According to wiki, "He later turned informant for the FBI, working with the agency for over ten months to aid them in identifying other hackers from Lulzsec and related groups"
The CIA's website went down June 15th, 2011 (towards the end of the LulzSec campaign) - definitely while Sabu was working for the FBI.