God never included desire and a form of baptism. And, to my knowledge (please correct me if I am wrong with this), the Church has never made an infallible statement about baptism of desire.
Continuation in defense of baptism by water, blood, and desire…
St. Alphonsus deLiguori…
Baptism, therefore, coming from a Greek word that means ablution or immersion in water, is distinguished into Baptism of water “fluminis”], of desire “flaminis” = wind] and of blood.
We shall speak below of Baptism of water, which was very probably instituted before the passion of Christ the Lord, when Christ was baptised by John. 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 of 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”.
Baptism of blood is the shedding of one’s blood, i.e. death, suffered for the Faith or for some other Christian virtue. Now this Baptism is comparable to true Baptism because, like true Baptism, it remits both guilt and punishment as it were ex opere operato. I say as it were because martyrdom does not act by as strict a causality “non ita stricte”] as the sacraments, but by a certain privilege on account of its resemblance to the passion of Christ. Hence martyrdom avails also for infants seeing that the Church venerates the Holy Innocents as true martyrs. That is why Suarez rightly teaches that the opposing view * is at least temerarious. In adults, however, acceptance of martyrdom is required, at least habitually from a supernatural motive.
Venerable Pope Pius IX, Quanto Conficiamur Moerore, August 10, 1863
And here, beloved Sons and Venerable Brethren, it is necessary once more to mention and censure the serious
error into which some Catholics have unfortunately fallen. For they are of the opinion that men who live in errors, estranged from the true faith and from Catholic unity, can attain eternal life. This is in direct opposition to
Catholic teaching.
We all know that those who are afflicted with invincible ignorance with regard to our holy religion, if they
carefully keep the precepts of the natural law that have been written by God in the hearts of all men, if they are
prepared to obey God, and if they lead a virtuous and dutiful life, can attain eternal life by the power of divine
light and grace. For God, Who reads comprehensively in every detail the minds and souls, the thoughts and
habits of all men, will not permit, in accordance with His infinite goodness and mercy, anyone who is not guilty of a voluntary fault to suffer eternal torments (suppliciis).
However, also well-known is the Catholic dogma that no one can be saved outside the Catholic Church, and that
those who obstinately oppose the authority and definitions of the church, and who stubbornly remain separated
form the unity of the Church and from the successor of Peter, the Roman Pontiff (to whom the Saviour has
entrusted the care of His vineyard), cannot attain salvation.
Pope St. Pius X, Catechism of Christian Doctrine, para. 132
A person outside the Church by his own fault, and who dies without perfect contrition, will not be saved. But he
who finds himself outside without fault of his own, and who lives a good life, can be saved by the love called
charity, which unites unto God, and in a spiritual way also to the Church, that is, to the soul of the Church.
Pope Pius XII, Encyclical Letter Mystici Corporis, June 29, 1943
From a heart overflowing with love, we ask each and every one of them [non-Catholics] to correspond to the
interior movements of grace, and to seek to withdraw from that state in which they cannot be sure of their
salvation. 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 be
enjoyed only in the Catholic Church.
Also, St. Thomas Aquinas defended belief in the three modes of baptism.*