The DAVD Conspiracy Theory was concocted by Agent Kayleigh Leonard. Put simply, this agent believed that the Disturbing Acts of Violence Department were up to No Good. She accused them of kidnapping and torturing her partner, Salamander, and of various other, well, disturbing acts of violence. Following the return of the Black Cats, she altered her theory slightly to claim that DAVD were working with the Cats, and had been since before the Reorganisation.
It is unknown whether Kayleigh is simply insane, or whether she was receiving echoes of the Mirror Multiverse's DAVD. The former explanation, however, may be more likely. It's also unknown if there are other proponents of the theory.