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St. Alphonsus never taught that people could be saved without Baptism.

Yes he  did. 
"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.”

St. Alphonsus Liguori 

That is not being saved without Baptism. It is the water being supplied by the "votum" at last minute for a dying cathechumen.

All other conditions required for salvation, (such as the truths that must be believed in), still apply, just as the obligation of receiving the water Baptism still remains if the catechumen lives and can make it.

Well sure. I thought when you said St. Alphonsus did not teach one could be saved without Baptism, you meant water Baptism. So you do hold to a limited form of BOD. Good. What do you think St. Alphonsus means when he mentions "implicit desire"?

Yes he  did.
"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.”

St. Alphonsus Liguori

St. Alphonsus completely misconstrues the authority of the "de presbytero non baptizato".  This was not a papal teaching to the Universal Church.  Otherwise, a very similar letter condemns as heretical his own teaching that people who are saved by BoD do not receive a complete remission of the temporal punishment due to sin.  St. Thomas excoriates the same Pope Innocent who in yet another similar letter promotes the heretical position that the Consecration at Mass can be valid even if the priest merely thinks the words of consecration.

As for the Council of Trent, the "cannot without" phraseology teaches necessary cause but not necessarily sufficient cause for justification.

I cannot stay alive without water.  True statement.   Does this mean that water alone suffices to keep me alive?  That I can live without also having food?  Of course not.  Same phraseology is used in Trent.

I cannot stay alive without food or water.  Does this mean that I cannot stay alive unless I have either food OR water?  Of course not.  It means that I cannot stay alive if EITHER one is missing.  And this sense is confirmed by the citation of Our Lord immediately after that no one can be born again without water AND the Holy Spirit.  Trent is making an analogy between the "laver" and Our Lord's water, and then between the "votum" and the Holy Spirit.  When Trent teaches about the votum being sufficient (along with perfect contrition) to receive remission of mortal sin, it explicitly uses the expression EITHER ... OR ELSE.  This phraseology is NOT present in the Baptism section.  So it does not teach the equivalent of "I cannot stay alive without either food or else water."