Glad that one of your professors upheld it. As for short-hand, Ladislaus, we can call it Thomism. Both proponents and detractors typically style it such, even though it is nothing other than the consecrated Tradition of the Fathers that St. Thomas merely collected and reaffirmed. It is also upheld in various Creeds taken by the Popes, that without the Catholic Faith no one is saved, and the Catholic Faith includes explicit faith at least in Jesus and His divinity.
“Some theologians hold that the belief of the two other articles - the Incarnation of the Son of God, and the Trinity of Persons - is strictly commanded but not necessary, as a means without which salvation is impossible; so that a person inculpably ignorant of them may be saved. But according to the more common and truer opinion, the explicit belief of these articles is necessary as a means without which no adult can be saved."
That Pope St. Pius X was a Thomist should in my opinion be sufficient for all informed traditional Catholics to be one. It is also taught by some manuals, as mentioned above. You criticize traditional priests for not teaching it today, but I think you forget this doctrine has fallen into confusion over the course of the last century, one reason for which is that many people think Suprema Haec favored the minority opinion, and others, such as Fenton, who gave it up not after Suprema Haec but after Vatican II. Today, there are only few priests, like your professor, who still read and learn entirely from the old manuals, and adhere strictly to Thomism. Some recent manuals also expressly favored the minority opinion, especially after Quanto Conficiamur Moerore.
But I've never known anyone who favors the minority opinion answer the proofs offered by St. Alphonsus, Fenton and Mueller, including the passages we've seen from Tradition, Pope Benedict XIV and Pope St. Pius X. They are a sufficient proof of Thomism, it is Tradition, it is tried and tested, and has good fruits.
we answer the Semipelagians, and say, that infidels who arrive at the use of reason, and are not converted to the Faith, cannot be excused ... St. Thomas explains it, when he says, that if anyone was brought up in the wilds, or even among brute beasts, and if he followed the law of natural reason, to desire what is good, and to avoid what is wicked, we should certainly believe either that God, by an internal inspiration, would reveal to him what he should believe, or would send someone to preach the Faith to him, as he sent Peter to Cornelius. Thus, then, according to the Angelic Doctor, God, at least remotely, gives to infidels, who have the use of reason, sufficient grace to obtain salvation, and this grace consists in a certain instruction of the mind, and in a movement of the will, to observe the natural law; and if the infidel cooperates with this movement, observing the precepts of the law of nature, and abstaining from grievous sins, he will certainly receive, through the merits of Jesus Christ, the grace proximately sufficient to embrace the Faith, and save his soul.”
There are many known examples where God has done extraordinary things to bring infidels to Christ, that have always surprised Christian missionaries.
Claude-Charles Dallet wrote of Caius of Korea in A history of the church in Korea, "His history proves, in a dazzling way, that God would rather make a miracle than abandon an infidel who follows the lights of his conscience, and seeks the truth with an upright and docile heart.
In The Victories of the Martyrs by St. Alphonsus de Liguori, it is said that "One day during sleep it seemed to him that the house was on fire: a little while afterwards a young child of ravishing beauty appeared to him, and announced to him that he would soon meet what he desired; at the same time he felt himself quite well, though he had been sick. Despairing of seeing among the bonzes the light for which he was longing, he resolved to leave them." ...
While he was instructed, one of the priests showed him a tableau representing Jesus Christ, at which Caius is said to have exclaimed,
"Oh! Voila! Here is who appeared to me in my cave, and who foretold all that happened to me."
As far as the possibility of material heresy in one who believes in Christ is concerned, almost all authorities admit it. Fr. Mueller writes, “Unquestionably, authorities in any number may be cited to prove – what nobody disputes – that pertinacity in rejecting the authority of the Church is essential to formal or culpable heresy" citing among others, St. Augustine who writes, "But though the doctrine which men hold be false and perverse, if they do not maintain it with passionate obstinacy, especially when they have not devised it by the rashness of their own presumption, but have accepted it from parents who had been misguided and had fallen into error, and if they are with anxiety seeking the truth, and are prepared to be set right when they have found it, such men are not to be counted heretics. Were it not that I believe you to be such, perhaps I would not write to you."
So, the case of a person who believes in Jesus (Trinity and Incarnation) and does not yet cling to any heresy is slightly different. He can for a short time be in a heresy that is purely material, which is not heresy properly so called, but only error. However, there is a great danger of him clinging obstinately to some heresy shortly after adulthood, or of otherwise falling into mortal sin and being unable to recover grace after that. Most theologians taught that a child coming to the age of reason in a non-Catholic sect can only remain for a short time within the Church. After that, he will likely formally become a heretic.
See also Fr. Arnold Damen, a friend of Fr. Mueller, who personally received some 13,000 Protestant converts into the Church, say something similar below.
http://www.olrl.org/apologetics/one_church.shtml