We're shown that everything Adam sees and hears is, or at least can be recorded various times in the story. Well, Adam saw some pretty incriminating stuff in Picus' secret offices; even if we assume he never saw any of the E-Mails in the computers in the level (which the dialogue does sometimes seem to suggest...) there's a room with a big screen built in to the wall depicting falsified news footage being rendered.
Since the source for the "supersoldier experiments" footage is Picus, and everyone at SI would presumably be interested in not being framed for what they're accused of, why doesn't anyone use the Adamcam's footage to damage Picus' reputation? They never even discuss the possibility.
They can't be concerned about the Illuminati knowing he was there, since he has to have left at least one corpse behind by the time he leaves anyway, and the enemies there talk about knowing Jensen is in the building. That's the only counterargument I can think of.