This is confirmed in chapter four of Trent’s Decree on Justification, which states that “This translation [i.e., justification], however, cannot, since promulgation of the Gospel, be effected except through the laver of regeneration [i.e., baptism] or its desire, as it is written: ‘Unless a man be born again of water and the Holy Ghost, he cannot enter into the kingdom of God’ (John 3:5).”
  

This is false. Trent teaches that the instrumental cause of justification is the Sacrament of Baptism. In order to avoid heresy one must confess that BOD is somehow a waterless mode of the Sacrament of Baptism.

Proposed; The Council of Trent in Session VI, the Decree on Justification; chapter 4 supports BOD. First I must state that the Dnz 796 of this decree is a willful mistranslation to favor BOD and that is a serious sin. Knowing this and still using it is a deception, and depending on circuмstances (who your trying to deceive) could be a serious sin as well. The latin word sine which means ‘without’ in English and has been mistranslated to ‘except through’ giving a different meaning.

Answer; Now on to the meaning. The fathers at Trent were battling the practice of forced baptisms, most recently in Spain, which is why they defined the remedy for original sin as they did. Trent states that justification cannot be effected without the laver of regeneration or the will to receive it. Notice that in using the term “laver of regeneration” they specify the form and matter alone and they did not say baptism or the will thereof. This is because they are stating unequivocally, that form, matter, and intent are necessary for the sacrament. The fathers then go on to quote John 3:5 as support and command us to take it literally. Think of any two things you know go together and then substitute them into the sentence and it makes perfect sense. A man cannot be married without a woman or the will to marry her. The BOD of desire proponent claims this chapter means either the laver of regeneration or the will to receive it are sufficient for justification so that the will alone (votum means will not desire) is sufficient but this means then that the laver alone, absent the will, is sufficient and this is falsified in the very next chapter in Trent. Rather than supporting BOD this chapter in Trent actually denies its possibility.

Then how could St Genesius be a saint?  

Some people would argue that there was not sufficient intent on the part of the actor performing the Baptism to qualify as valid intention.  I think that's debatable.  If he thought he was DOING a ceremony DONE by the Church, I argue that it was valid.  Church has never stated that the person baptizing must believe in the effect of the Sacrament, which is why even atheists can validly baptize.