Pius X re-emphasized this prohibition on the ground that women were not permitted to fulfil any liturgical function (Motu proprio ‘De musica sacra’, 1903).
No, the original SSPX, Archbishop Lefebvre, etc. are not dumber than you. They are well aware of those quotes forbidding women in "choir".
The "choir" spoken of in that prohibition is a completely different animal than the thing you call a "choir" at your local Trad chapel. That is the short version.
I've answered this question in depth before, but with all the activity and traffic on CathInfo, I can't find it at the moment.
If the singing isn't liturgical (an official part of the liturgy; as in, the priest doesn't have to repeat it up there at the altar) then it's just a lay choir, and that's completely different.
The prohibition is about liturgical choir, as in "choir stalls" that monks or seminarians sit/kneel/stand in while they recite the Divine Office (the official, public prayer of the Church). Example sentence, "Sister Mary was in Choir reciting Terce when the bishop arrived at the convent."
It's a confusion of terms. Sometimes a term can mean two completely different things.
For example, the term "anti-semitism". It depends on who is defining it.
Anti-semitism (hatred of a human being because he is Jєωιѕн) is a grave sin.
Anti-semitism (opposing the errors of Judaism, and/or the agenda of the Jєωs following the тαℓмυd and trying to bring about the One World Government of the Antichrist) is a virtue.
This is a good example of why reading a single book doesn't make one an expert. A person with high intelligence might assume that because he can read and understand English that he knows how to interpret or apply a given sentence that he reads somewhere.
That's not always the case.