I never said it wasn't the same thing (fruitless-without fruit). You had just said the only way to translate sine was to without.
After all...
...any Latin scholar will tell you that sine means without.
In each circuмstance, the word was altered because it would have altered the meaning of the text, or made it, for lack of a better term, wrong.
Or how sayest thou to thy brother: Let me cast the mote without of thy eye; and behold a beam is in thy own eye?
It makes perfectly good etymological sense, if you will, to translate sine to 'except through', especially if we are defending baptism by blood or desire. (As all the great Church doctors did.)
Applying a law that would not have been used by Trent, thereby altering the original meaning of the decree, puts us at odds with what has always been taught by the Church, and at odds with another decree itself, that we are to maintain the dogma's in the sense they were proclaimed.