The Feeneyites got themselves in trouble over Baptism of Desire. That is what the Protocol Letter from the Holy Office addresses.
Boniface VIII's Bull is referring specifically to the Greeks of the Empire, who at that time were quite resistant to the whole notion of the Venetians coming in and lording it over them and forcing their heirarchy to become Latin. The denial put forth by the Greeks at that time was a novel claim arising from this agressiveness that St. Peter had somehow not been entrusted with the Church in the East, because they certainly wanted no part of what St. Peter's sucessor was attempting to impose on them through armed force.
The correct question of course, is not whether or not St. Peter was entrusted with the whole Church, but what that entrustment allows St. Peter to do. That is the true difference between East and West up until now.
"The correct question of course, is not whether or not St. Peter was entrusted with the whole Church, but what that entrustment allows St. Peter to do. That is the true difference between East and West up until now."
Well, there are and have been theological differences, some actually quite important at various levels. Most of those, however, have been looked at and not been determined to be insurmountable obstacles for one reason or another. Some, like the filioque, have had their explanations expressed anew to avoid problems while others, like the differences between Latin and Palamite theology on grace and the Holy Spirit are so arcane that perhaps 1 in 10,000 lay people even know what either of them are, let alone why they are important (and they are important).
Otherwise, your comment is pretty much spot on.