I didn't get that sense (James the Righteous doesn't really come across as a mobster in Acts 15, but to each his own), but your point that he feared the Men of James come to Antioch frankly makes the matter worse... now we have a supposed "Pope" who is genuflecting not just to a mere bishop, but to the bishop's itinerant subordinates.
Are these the actions of one who himself holds administrative Supremacy in the Church? Put simply... no. They are not.
Anyway, Paul chastises him for *failing* to issue doctrine, not for issuing a false one. When we read about the case in Acts, we find that Peter issues a doctrine, and the rest of the apostles consent to it. Now if Peter doesn't rank above Paul, why doesn't Paul do correct them himself? Rather, Paul appeals to the authority (Peter) to issue decide the matter.
There's no record that Paul appealed to Peter(and we certainly have record of Paul "appealing to authority" in cases when he actually did so!).
Peter then corrects the bishop whose diocese it is (James), who then corrects his presbyters (priests).
Peter does not address himself to James. What is more, the presbyters, after listening to Peter say his piece on the subject, turn their attention to listen to Paul and Barnabas some more (Acts 15:12).
So what we have here... Paul and Barnabas speak. Then Peter speaks. Then Paul and Barnabas speak some more.
Then James rules his judgment upon the matter... and everyone does what James says. (James has spoken; the matter is at an end).