Aside from the very direct accusation against Sweep, what he's doing is trying to funnel everybody over to Barnes's coverage. That way it will plant in people's (again: idiots) minds that he is the victim of a conspiracy, without him actually claiming he is.
This is why I say he's basically abdicated a lot of his defense to Barnes's insanity. The choice of Frank White to represent him is the biggest evidence of that. Frank was not picked out of a hat. He lives and works some distance away from Nick, and I doubt he was anywhere near the most accomplished lawyer that Nick could have gotten. He's Nick's lawyer because he's a Barneswalker.