Personally, I would have no trouble believing Section 31 allowed all those records to be released, and the public to find out about the organization, let agents and operations get revealed, and then let people think the organization has been abolished.
Sounds about right. Assuming Section 31 was in on the Khitomer Conspiracy, then they just let people like Admiral Cartwright and Valeris take the fall. Or they just let Admiral Pressman and others take the fall for getting caught experimenting with an illegal phasing cloak.
Perhaps Daniels is a member of a 31st century version of Section 31. At least, that's the theory on YouTube and the premise of a fan fiction series outlined on the Expanded Universe wiki.