TIA's theological "argument". It always helps to lay things out as a syllogism to expose the faulty logic.
Major: God is good.
Minor: It would be bad if God were to allow those who had no chance to know the truth an alternative means of salvation than Baptism.
Conclusion: Such an alternative means must exist (i.e. BoD).
So the argument rests essentially on the Minor, since no one denies the Major.
So BoDers claim that in denying the conclusion, "Feeneyites" deny the Major. When the reality is that we deny the Minor. As some here on CI have been fond of claiming, we deny the Mercy of God. Hogwash.
We actually believe that God gives all people the opportunity to be saved and that if they do not arrive at a knowledge of the truth it's because they placed some obstacle in the way of God's grace which would lead them to that knowledge.
THAT is in fact the teaching of St. Thomas, that such are not punished for the sin of infidelity, but for other sins, that if such as these would place no obstacles in the way of the working of God's grace, God would in fact enlighten them with the knowledge necessary for salvation ... even if necessary by miraculous means. That is also the meaning of the teaching of Pope Pius IX that is always warped by the anti-EENS crowd. In other words, the perennial Catholic teaching that explicit knowledge of God is required for supernatural faith and therefore for salvation stands. The way these people construct the syllogism outlined above, you would think that salvation is possible without any knowledge of God whatsoever ... and that's heresy. They would turn Pius IX into a Pelagian heretic.
This argument is also predicated on the heresy that it could ever be "impossible" for God to provide the Sacrament. BoDers argue that Feeneyites constrain God with the Sacraments, but the reality is that the BoDers constrain God with "impossibility". It is not we who constrain God with the Sacraments, but God who constrains us with them, and He can and will in His Providence provide the Sacrament to His elect.
BoD theology is complete garbage that's predicated on one false premise after another, and it makes a mockery of God's providence. That's how faulty is the "reasoning" behind it. It's not theological reasoning at all, but emoting, emoting in the same category as those who shake their fists at God for being unmerciful when some tragedy befalls them. We most certainly believe that God is Merciful; we just disagree on how His Mercy works in the hearts of men.