Not sure who concocted this nonsense, but to the extent that +Lefebvre adhered to it, he was wrong.
Ministers need merely intend to do what the Church does and not to intend what the Church intends. Doesn't matter a lick if some bishops ordains a priests while not believing that ordination confers a character or has any ontological effect. That's why a faithless atheist can validly baptize.
Pope Leo XIII taught quite clearly that the intention is always presumed and that it belongs properly to the internal forum, but SSPX invented this fakery, the sleight of hand.
Bogus Ordo Ordinations are utterly null and absolutely void ... per the teaching of Pope Leo XIII, with the BS from these Modernist trolls notwithstanding. This has been demonstrated repeatedly and cannot be refuted ...
... and all we get is these clowns with their "muh Lefebvre" position.
Leo XIII stated that the intention of the ministers belongs to the internal forum, cannot be known by the Church, and is always presumed to be there. Theologians, furthermore, add that the requisite intention is simply to do what the Church does. If the minister is conscious of the fact that, "yep, this is the Catholic Rite, and, yeah, I'm putting on my vestments now, and am going to go out there to do it" ... he has the requisite intention. Nor is SSPX in any position to "investigate" squat, since even the Church doesn't presume to know the internal forum.
SSPX pretend that doing a conditional can only be justified if one has conducted an investigation with the same rigor as one might investigate a marriage annulment. That's ridiculous. Any prudent doubt suffices, and nobody's required to spend hundreds of man-hours "investigating" something that can't be investigated anyway.
It's entirely certain that there's positive doubt about the Novus Ordo Rite of Ordination. Period. And there's no reason NOT to perform conditionals on all Novus Ordo presbyters ... except that the SSPX are playing politics and subjecting the faithful to invalid Sacraments from fake priests who go around simulating Masses.