The Orthodox are just as Catholic as the Melkites, not only in my opinion, but in the opinion of the Melkite Synod as well. And who says one has to be united to the Pope to be Catholic? In the centuries when the West saw two, and sometimes three Popes, who was to say at which moment which Western Christians were Catholic and which war not? There is more to Catholicity than mere papism.
Dear Stuart, if that is true, why is there this division between Churches that have one group in union with Rome and an Orthodox counterpart not in union with Rome? (My own answer is that unity with Rome *is* important, but I sincerely wonder why the Melkites endure division from the Antiochene Orthodox if the issue isn't important?)
Also, when there was confusion about who was Pope, everyone still had to believe it was important to be in union with the Pope, even if you weren't sure who the man was, you had to acknowledge unity with the office. There were never "two, and sometimes three Popes" by the way, just one, and the others were anti-Popes.