The problem is that you erroneously interpret implicit desire contrary to Trent. Go re-read the entire Session 6. I'll post part of Chapter VI below:
http://www.thecounciloftrent.com/ch6.htmCHAPTER VI. The manner of Preparation.Now they (adults) are disposed unto the said justice, when, excited and assisted by divine grace, conceiving faith by hearing, they are freely moved towards God, believing those things to be true which God has revealed and promised
(Incarnation, Original Sin, Trinity, Redemption...not just one of these, but ALL OF THEM),
-and this especially, that God justifies the impious by His grace, through the redemption that is in Christ Jesus; and when, understanding themselves to be sinners, they, by turning themselves, from the fear of divine justice whereby they are profitably agitated, to consider the mercy of God, are raised unto hope, confiding that God will be propitious to them for Christ's sake; and they begin to love Him as the fountain of all justice; and are therefore moved against sins by a certain hatred and detestation, to wit, by that penitence which must be performed before baptism:
(So penitence MUST be part of this implicit desire for the Faith. A generalized "belief in God" or a desire to "do what God wants" is not sufficient.) lastly, when they purpose to receive baptism, to begin a new life, and to keep the commandments of God.
(The desire for Baptism can be implicit, in the sense that it is "implied" by actions and not VERBALLY expressed, but that does not mean that the desire is unexpressed, for Trent says that one must purpose/decide to receive baptism, to begin a new life (i.e. turn from sin) and keep the commandments. This means that the person, in his heart, must WILL that baptism be received, even if he does not explicity tell anyone else, though by his actions, it is implied what he wants (i.e. he takes catechism classes).