Right. The intention of the priest/bishop DOES NOT MATTER. What matters are the WORDS of the rite. The WORDS of the rite = the Church's intention. The Church's intention is all that matters.
The new rite changed the WORDS, therefore the intention (of the words) changed. Therefore there's doubt.
The new-sspx/indulters want to concentrate on the PERSONAL intentions of the priest/bishop. This is bad theology and is irrelevant.
Yes, Pope Leo XIII made this very clear in
Apostolicae Curae.
33. With this inherent defect of “form” is joined the defect of “intention” which is equally essential to the Sacrament. The Church does not judge about the mind and intention, in so far as it is something by its nature internal; but in so far as it is manifested externally she is bound to judge concerning it. A person who has correctly and seriously used the requisite matter and form to effect and confer a sacrament is presumed for that very reason to have intended to do (intendisse) what the Church does. On this principle rests the doctrine that a Sacrament is truly conferred by the ministry of one who is a heretic or unbaptized, provided the Catholic rite be employed. On the other hand, if the rite be changed, with the manifest intention of introducing another rite not approved by the Church and of rejecting what the Church does, and what, by the institution of Christ, belongs to the nature of the Sacrament, then it is clear that not only is the necessary intention wanting to the Sacrament, but that the intention is adverse to and destructive of the Sacrament.
So it's not the intention of the minister (which is by its nature internal) ... and which is presumed if the Catholic Rite is used ... but the intention of the Rite that's in question. If the Rite is changed with the "manifest intention ... of rejecting what the Church does", then this invalidates the intention of the Rite, regardless of what the minister intends in the internal forum.
Earlier, he wrote about the intention of the Rite, i.e. the reason it was composed ... and his words could hauntingly be applied verbatim to the Conciliar Rites:
30. For the full and accurate understanding of the Anglican Ordinal, besides what we have noted as to some of its parts, there is nothing more pertinent than to consider carefully the circuмstances under which it was composed and publicly authorized. It would be tedious to enter into details, nor is it necessary to do so, as the history of that time is sufficiently eloquent as to the animus of the authors of the Ordinal against the Catholic Church; as to the abettors whom they associated with themselves from the heterodox sects; and as to the end they had in view. Being fully cognizant of the necessary connection between faith and worship, between “the law of believing and the law of praying”, under a pretext of returning to the primitive form, they corrupted the Liturgical Order in many ways to suit the errors of the reformers. For this reason, in the whole Ordinal not only is there no clear mention of the sacrifice, of consecration, of the priesthood (sacerdotium), and of the power of consecrating and offering sacrifice but, as we have just stated, every trace of these things which had been in such prayers of the Catholic rite as they had not entirely rejected, was deliberately removed and struck out.
How is this not exactly what Montini et al did? They associated with abettors from the heterodox sects (the Prot ministers helping to write the NOM, anyone?), using the pretextt of returning to the primitive form (check!), they corrupted the Rite to "suit the errors of the reformers" (again check!) No only is there no clear mention of sacrifice, preisthood, etc. ... but every trace of these things which had been in the Catholic Rite was deliberately removed and struck out. These words of Leo XIII are prophetic and could have been applied verbatim to the NOM.

31. In this way, the native character or spirit as it is called of the Ordinal clearly manifests itself. Hence, if, vitiated in its origin, it was wholly insufficient to confer Orders, it was impossible that, in the course of time, it would become sufficient, since no change had taken place. In vain those who, from the time of Charles I, have attempted to hold some kind of sacrifice or of priesthood, have made additions to the Ordinal. In vain also has been the contention of that small section of the Anglican body formed in recent times that the said Ordinal can be understood and interpreted in a sound and orthodox sense. Such efforts, we affirm, have been, and are, made in vain, and for this reason, that any words in the Anglican Ordinal, as it now is, which lend themselves to ambiguity, cannot be taken in the same sense as they possess in the Catholic rite. For once a new rite has been initiated in which, as we have seen, the Sacrament of Order is adulterated or denied, and from which all idea of consecration and sacrifice has been rejected, the formula, “Receive the Holy Ghost”, no longer holds good, because the Spirit is infused into the soul with the grace of the Sacrament, and so the words “for the office and work of a priest or bishop”, and the like no longer hold good, but remain as words without the reality which Christ instituted.
32. Many of the more shrewd Anglican interpreters of the Ordinal have perceived the force of this argument, and they openly urge it against those who take the Ordinal in a new sense, and vainly attach to the Orders conferred thereby a value and efficacy which they do not possess. By this same argument is refuted the contention of those who think that the prayer, “Almighty God, giver of all good Things”, which is found at the beginning of the ritual action, might suffice as a legitimate “form” of Orders, even in the hypothesis that it might be held to be sufficient in a Catholic rite approved by the Church.
So not only did changes they tried to introduce later not rescue the Rite, since it was vitiated in its Origins (due to the initial intention of removing Catholic elements to appease the heretical sects), but Leo XIII absolutely and expliciltly rejects the argument (first bolded section above) that it CAN BE UNDERSTOOD AND INTERPRETED IN A SOUND AND ORTHODOX SENSE. In other words, it's ambiguous and CAN be understood in a Catholic sense ... the very position of SSPX, where then with the proper "internal" intention that nobody, not even the Church, can even know about, it could be rendered invalid.
So in the context of this Rite that was intended to reject the clear sense of the Catholic Church regarding the Rite (second bolded section), any argument that this or that section COULD suffice to legitimately express the Catholic meaning is rejected due to the overall context of the Rite.
So, the Rite, the reason it was composed, where Catholic elements were removed, etc. rendered the intention of the Rite invalid and not salvageable by someone who would impose some Catholic interpretation onto some ambiguous element within it. That overall context vitiates any ambiguous sections that could be Catholicized by the right intention.
You'd think the SSPXers had never read
Apostolicae Curae, one of the most comprehensive explanations of Catholic theology available regarding the validity of Rites and stamped by Magisterial authority.