I always wondered if this scene was not a delusion and simply a catalyst that triggered his future delusions. We don't actually see Parcher, a known delusion, until after he's done with this first code-breaking scene and when Nash nods to Parcher and asks about "big brother" the people in the room glance that way and don't respond at all. It's as if they didn't see anyone there and just shrugged off an odd, nonsensical question.