I don't think our readings are different at all, since you appear to be saying the same thing I am - that the force of the words is aimed at those who deny all entrustment of a particular group to St. Peter, not those who dispute what such an entrustment gives St. Peter's successor the right to do.
Therefore, this declaration is not aimed at the Orthodox and other Easterners who accept the primacy of Rome over the whole Church in some sense, nor is it aimed at Anglicans or Lutherans in a similar position.
The bull makes several simple definitions and draws several simple theological conclusions.
1) There is one Church
2) It is Catholic and Apostolic
3) There is no salvation outside it
4) There is no remission of sins outside it
5) All members of the Church were entrusted to St. Peter
Conc.) Therefore those who deny being entrusted to St. Peter are not part of this one Church.
6) The spiritual power of the Church stands in judgement of the moral conduct of the temporal power of the state
7) This power is held by St. Peter and his successors by commandment of Christ giving power to bind and loose
8) It is necessary for salvation for all to be subject to St. Peter's successors.
It really is a very clearly different thing to say as a Protestant does that there is not one Church, the Pope is not the head of it, and we are certainly not subject to him, and to say as the Orthodox and Anglo-Catholics do that the Pope is the head of the Church being its first primate, and we would like to be subject to him, but we fear his lording it over us like a slave-driver as some Popes have attempted in the past.
The Protestant is unwilling to live unity in charity with his fellow Christians, therefore he is empty of charity. The Anglo-Catholic and Orthodox are already living unity in charity, since they profess the same faith, celebrate the same sacraments, and have a desire to be completely united under the same head.
It is impossible to see how the proclimation of Unam Sanctum would condemn a group such as the Tradtional Anglican Communion or Forward-In-Faith, which although not formally part of the Catholic Church, nevertheless wishes to be and recognizes the Pope as Pope.
Unam Sanctum is aimed at those who deny the truths of the faith contained in St. Matthew 16 and St. John 21.
"6) The spiritual power of the Church stands in judgement of the moral conduct of the temporal power of the state
7) This power is held by St. Peter and his successors by commandment of Christ giving power to bind and loose
8) It is necessary for salvation for all to be subject to St. Peter's successors."
As to 6 & 7, Orthodoxy believes this power is given to all the bishops who rightly teach The Faith (Matt 18:18). Orthodoxy I suppose accepts 8 in the sense that proper ecclesiology requires that the Pope of Rome be the "leader among (but not over) the bishops". On the other hand, the conclusion in 8 is at least arguably problematic from an Orthodox pov since +Peter's position as primus is quite clearly dependant on his profession of faith (Matt 17). If the Pope should abandon the Faith, then of course he cannot exercise that primacy. Certainly Rome doesn't believe it ever abandoned the Faith, but the other four patriarchates believe that is in fact what happened. It seems likely that both "sides" have "adjusted" their positions over the past 100 years or so; certainly the enthusiam one sees in Orthodoxy, even among educated laymen and lower clergy, for +BXVI would seem to indicate something of a sea change in relations between these particular churches. And I must say the respect and reverence for Orthodoxy evinced by so many Latin Rite Catholics bodes well for the future.