There are a few pretty dangerous lines in the Haos Doctrine, if they are taken as absolute:
These people sent humanity to senseless wars with the blood of men on everyone's hands.
They utilize logic against logic, keeping the promised knowledge from us. The new millennium has passed and we are more ignorant than ever.
Only we can change this stagnant world.
You know, if they are absolutely loyal to the document than they would almost have to rebel. I brought up a similar problem when "the Golems" were written. Our founding documents really do not explain how the insurgency became a strictly hierarchical military.
There is also this nugget from mission statement that might blow up in our face:
We must enslave humanity before they enslave us.
The Insurgency AI projects are as far as I know
Things that can be found on the main site
spelunker.ai (arbiter of deleted files)
Quaesitor (Orbital Surveillance)
The a deleted AI we had but no long have
Anderson (ship) (Sub-Marine that also simulates a civilian)
Several of my own files that were never published
Mr. Lolz (Financial backer)
BMS (and related off-shots) (general management)
Galetea (future assistant)
Also there are some SCP articles that mention the Insurgency, as well as the Containment Breach games, in which a computer anomaly is working with insurgency agents.
Which one would fit your intended story purpose?