Faith can be implicit for baptism of desire, because God can discern whether it is implied. Man cannot know, so it is ordered that before someone baptizes another, there must be expressed an explicit faith.
So an idol-worshipper can receive baptism of desire, even though he does not desire baptism at all and does not believe in Jesus Christ and the Trinity. Nobody ever taught that - St. Alphonsus and St. Thomas Aquinas who taught BoD also taught necessity of explicit faith for salvation, they did not support your heresies.
By the way, that pagan with "implicit faith" has to be in the Church for salvation (for we know that there is no salvation outside the Church). So the Church constitutes both of members of visible Catholic Church, and of pagans from different false religions who have "implicit faith". One could say that the Church of Christ
subsists in the Catholic Church - Vatican II ecclesiology.
Again, the Athanasian Creed:
"Whosoever will be saved, before all things it is
necessary that he hold the
Catholic Faith. Which Faith except everyone do keep whole and undefiled, without
doubt he shall perish everlastingly.(...) He therefore that will be saved, must thus think of the Trinity. Furthermore, it is
necessary to everlasting Salvation, that he also believe rightly the Incarnation of
our Lord Jesus Christ."
So, to be saved, one must:
1) think of the Trinity (you can't think about something you never heard of - that rules out implicit faith)
2) keep the Catholic faith whole and undefiled (you can't keep whole and undefiled something you never knew about - again, rules out implicit faith).
In other words, a belief that people can be saved without explicit faith in Christ and the Trinity constitutes rejection of the Athanasian Creed and thus a heresy.
It also constitutes rejection of Cantate Domino which teaches that all who die as pagans go to hell. According to implicit faith theory some pagans can be saved if they are invincibly ignorant, which is contrary to the Council of Florence.