First, papal infallibility doesn’t depend on whether something is a Bull or verbal statement. The delineation between kinds of papal documents did not exist for much of the early centuries of the Church–yet papal infalliblity is al ways true. According to the definition from the First Vatican Council (and it’s restatement by the Second), all that is necessary is that the pope definitively declares a teaching to be held by the universal Church. That’s it
Boniface VIII’s statement is correct in that it requires that it is necessary for salvation to be subject to the Roman Pontiff–that is united to the Universal Church governed by him.
This teaching was repeated by Bl. John XXIII:
“The Saviour Himself is the door of the sheepfold: ‘I am the door of the sheep.’ Into this fold of Jesus Christ, no man may enter unless he be led by the Sovereign Pontiff; and only if they be united to him can men be saved, for the Roman Pontiff is the Vicar of Christ and His personal representative on earth.” (Pope John XXIII, homily to the Bishops assisting at his coronation on November 4, 1958Papal Teachings: The Church, Benedictine Monks of Solesmes, Boston, St. Paul Editions, 1962, par. 1556.)
Now, let’s look at the Pius XII statement. Obviously baptized kids and others who believe doctrinal error due to poor catechesis or whatever are not excluded from the Church. Same goes for other Baptized individuals suffering from the same ignorance. They “have not been so unfortunate as to separate themselves from the unity of the Body, or been excluded by legitimate authority for grave faults committed.”
Likewise, he is discussing the Church in terms of a visible Body and those are members of the Body–these are openly professing Catholics. But there are those who are united to the Soul of the Church, namely the Holy Spirit of which he says:
“Finally, while by His grace He provides for the continual growth of the Church, He yet refuses to dwell through sanctifying grace in those members that are wholly severed from the Body.”
Are all non-Catholics wholly severed from the Body? According to Pope Pius XII, they are not:
“For even though by an unconscious desire and longing they have a certain relationship with the Mystical Body of the Redeemer, they still remain deprived of those many heavenly gifts and helps which can only be enjoyed in the Catholic Church. Therefore may they enter into Catholic unity and, joined with Us in the one, organic Body of Jesus Christ, may they together with us run on to the one Head in the Society of glorious love.”
He expresses this more explicitly in his encyclical
Summi Pontificatus:
“Nor can We pass over in silence the profound impression of heartfelt gratitude made on Us by the good wishes of those who, though not belonging to the visible body of the Catholic Church, have given noble and sincere expression to their appreciation of all that unites them to Us in love for the Person of Christ or in belief in God.”
St. Alphonsus Liguori, Doctor of the Church, explains this idea of being united to the Spirit in this way (citing the Council of Trent):
“But baptism of desire is perfect conversion to God by contrition or love of God above all things accompanied by an explicit or implicit desire for true Baptism of water, the place of which it takes as to the remission of guilt, but not as to the impression of the [baptismal] character or as to the removal of all debt of punishment. It is called ‘of wind’ ‘flaminis’] because it takes place by the impulse of the Holy Ghost Who is called a wind ‘flamen’]. Now it is de fide that men are also saved by Baptism of desire, by virtue of the Canon ‘Apostolicam De Presbytero Non Baptizato’ and the Council of Trent, Session 6, Chapter 4, where it is said that no one can be saved ‘without the laver of regeneration or the desire for it.’”