The PERSONAL/INTERNAL intention does not affect sacraments, or else an atheist could not validly baptize. An atheist surely doesn't have ANY intention towards the sacraments, but he can still baptize. Why? Because the CHURCH'S INTENTION IS ALL THAT MATTERS.
There is no positive doubt in regards to +Thuc ordinations...the only *possible* exception being the Palmaranians in Spain... Outside of this, all of his Traditional rites were witnessed, and were involving other priests who were there. They had no positive doubts. They are eye witnesses.
Minor nitpick (If you are reading this, Tom, I say "minor" because it does not negate anything else said in the post above), but intention on part of the administer is required:
Trent Sess. VII
ON THE SACRAMENTS IN GENERAL
CANON XI.-If any one saith, that, in ministers, when they effect, and confer the sacraments, there is not required the intention at least of doing what the Church does; let him be anathema.
An atheist can, and must, have the proper intention in administering baptism..but "intending to do what the Church does" simply means that he wills to perform the rite as the Church does..I.e. baptizing someone with water, in the name of the Father, the Son, etc.
Now considering that +Thuc administered the sacraments with proper matter and form, and that there is no (zero (0), zip, zilch, nada, etc., etc.) evidence that +Thuc made known that he had a manifest contrary intention while performing the consecrations, it is presumed (
by the Church) that he had, at least, the intention of doing what the Church does in performing the consecrations.
A reference in The Angelus to an undated, untitled letter, with zero direct quotes, that +Thuc
allegedly published (and to this day has
never been found) claiming that he had a contrary intention in no ways establishes positive doubt. Not to the Palmar consecrations which the alleged letter concerned, and especially not to any other consecrations he performed