Of course, last I checked, the resistance of the Greeks was not over St. Peter and his sucessors being entrusted with the whole Church, but rather what that entrustment gave them liberty to do. Otherwise, Holy Father's such as St. John Chrysostom would have to be cast into the outer darkness with the wicked Latins.
And if any should say, "How then did James receive the chair in Jerusalem?" I would make this reply, that He appointed Peter teacher, not of that See, but of the whole world. (St. John Chrysostom, Homilies on John 83.1)For those things which are peculiar to God alone, (both to absolve sins, and to make the church incapable of overthrow in assailing waves, and to exhibit a fisherman that is more solid than any rock, while all the world is at war with him), these He promises Himself to give; as the Father, speaking to Jeremiah, said, He would make him as "a brazen pillar and a wall" (Jeremiah 1.18); but him only to one nation, this man in every part of the world. (St. John Chrysostom, Homilies on Matthew, 64.3)
During the time of controversy during which Unam Sanctum was written, the objection of the Easterners was that they would be more than happy to obey if only Rome would prove its faithfulness to Christ by casting out the filioque and other controverted items.
Did I say something was fictional? If your point is that Orthodoxy, throughout most of the past 2100 years was quite content with Petrine primacy exercised by a Pope who taught the orthodox Faith of The Church, well you are absolutely right. That would be true today, especially so with +BXVI on the throne of +Peter. That's why the discussions going on between our theologians with the support and backing of the Pope and Patriarchs is focused on defining the appropriate exercise of that primacy which is clearly something more than a mere primacy of honor. How much more is the issue. So far as I have been informed, they are looking to agree on what that exercise looked like, in a practical way, say before the Photian Schism. There are disagreements, I'm told, on that though not truly profound ones. One bright light here is that the world of the 21st century is a different place from that of +Photius and +Nicholas I and the involvement of hierarchs in government and vice versa much diminished.