Also in the link ...

Considering the Sacrament of Confirmation specifically, we must remember that, on the one hand, it is one of the sacraments which imprint a character upon the soul, and which thus cannot be repeated absolutely without sacrilege. On the other hand, it is not one of those which are strictly necessary for salvation. Thus to be justified in receiving it again conditionally ...
So he's claiming that because Confirmation is not strictly necessary for salvation, to be justified in receiving it ... different criteria apply.
Nonsense. If you have any kind of reasonable / positive doubt whatsoever, conditional administration may certainy be JUSTIFIED. Maybe not "strictly required", but certainly justified.
So it's also been part of the propaganda on this point to overemphasis the requirements of administering Sacraments conditionally because ... oh, it would be a sacrilege to confer these Sacraments again. Yes, but, ahem, THAT IS WHY THE CONDITIONAL FORMULA IS USED. Consequently, there's no risk of scacrilege whatsoever in using the conditional formula. What Trent was saying is that you cannot go around willy-nilly conditionally readministering Sacraments to anybody with a pulse, i.e. for any negative doubt whasoever. "Father, what if my Baptism was invalid. Please give me conditional Baptism." ... although even there, if the individual were experiencing some traumatic crisis of faith, scrupulosity, despair, etc. ... it might be justified to do it for those reasons along, but one should do it privately.
But any even moderately legitimate reason would justify it. Even the SV priests have exaggerated the requirements for conditional administration, where they have to engage in some quasi-thorough investigation, almost as if you were researching a marriage annulment. Utter nonsense. There's no such requirement. It suffices that it's well known that there's a tendency in the Novus Ordo to tinker with Sacraments, adlib the form, mess with the matter, etc. That by itself suffices. You are not required to spend resources and even money that you don't have to do investigations that are likely impossible anyway to reach a conclusion on since most of these situations took places years and even decades ago.
This is more than adequate: "Novus Ordo has this attitude about messing with Sacraments. I don't have time to research this case and souls have more important needs I should be attending to."
THEN, however, with Holy Orders, for instance ... there's ABSOLUTELY some serious positive doubt about them. That in turn leads to serious positive doubt about NO Confirmations just due to the doubt about whether the NO bishops are valid, and then even if the NO priests are invalid (having been ordained by NO bishops). Even if you could make a case that a priest with authority could validly confirm, we're not even 100% sure he's a valid priest.
Probably the one case where you wouldn't just administer the Sacraments without further inquiry would be people who had received the in the Eastern Rites, or, say, a legit Orthodox Rite (vs. the weird auto-cephalous ones nobody can even trace) ... with the one exception where if people had been baptized as adults, I've seen the old "hair baptisms" even in Eastern Rite, where they just poor some water on someone's thick hair and you're not entirely sure if it even touched their skin.