I always thought that RZC was a constitutional barony. Which would make Gryphon very much not head of state, even if he ran things.
That said, it wouldn't take much for Earth Alliance to make the connection between Gryphon, the WDF, and Zeta Cygni. They'd probably have Sonset Truthers on ISN, saying that Ben Hutchins always was the Butcher, and that his attempts at diplomacy are a cover for until he carries out his eeevil plan. Obviously humanized Salusians are just infiltrating Earth to destroy it. It's all connected! (Join Night Watch)
I guess I'm not reading for a story like that. But I do miss Redneck's writing because he did have some sense of politics going on in the background of his stories. Not sure if I'd agree with him in person on politics though -- it's better to let Zeta Cygni be a shining beacon of tolerance and democracy and security, and not think too much about the poor underclass living in those civil defense tunnels below New Avalon.
Really though, I suspect ZC acts like any other post-scarcity economy: basically like Star Trek.