No, mas. Pope I did not referee a throw down between Paul and James. And wait a minute, if he did, why did they not capitulate to him? He would have been considered infallible, right?
The throw down at the council was between the former pharisee Judaizers and the united position of Peter, Paul, and James. However, James appears to have been connected with the Judaizers:
Gal 2: 11 But when Peter was come to Antioch, I withstood him to the face, because he was to be blamed. 12 For before that certain came from James, he did eat with the Gentiles: but when they were come, he withdrew and separated himself
Peter, James, and the whole Church were eventually won over by the arguments of Paul. Peter appears to have been the bridge-man between Paul and James. The primacy of Peter did not require him to originate everything, only that he determine and authenticate whatever became official teaching. This is what Peter did in siding with Paul.
Peter was the oldest of the Apostles while the younger Paul was not even one of the twelve. It is unlikely that James, Patriarch of Jerusalem, would have capitulated to Paul without the influence of Peter.