I don’t think so, because:
1) The TIA letter alleges it has evidence in des Lauriers’ letter against the contention “That he had never said the New Mass – today it has become evident that he said it for many months,..”
2) The 16 page rebuttal of Madiran to des Lauriers concerns the latter’s charge that Lefebvre said the new Mass (not one of the transitional missals of 1963-1969).
Both are alleging Lefebvre said the Novus Ordo.
OK. The des Lauriers letter, on its own, still looks vague.
But I agree Madiran's rebuttal is specifically about the N.O.M.
A few points from Madiran's rebuttal:
1. des Lauriers letter alleges the Archbishop said the "innovated Mass" from April 1969 to 24 Dec 1971. Madiran says the N.O.M. was only permitted/required starting in November 1969, so the chronology in the letter is silly. [April 1969 is the date of Paul VI's constitution. It is my understanding that the first complete typical editions of the Paul VI Mass were not published until March 26, 1970.]
2. The rebuttal ends with a note from Abp. Lefebvre from 3 June 1979 saying "I can affirm that I never celebrated the new Mass according to the rite introduced in November 1969."
3. Madiran quotes another letter from des Lauriers from June 29, 1979 [I'm guessing this is referring to the note of 3 June]
You say you never celebrated the innovated mass. I give thanks to God and I am very happy. I maintain however the veracity of the observed facts that I related, while rectifying one error of date: the incident of Christmas happened in 1970, and not 1971. But I must conclude, celebrating the traditional mass, you have made external gestures that induced thinking that you celebrate the innovated mass.
So the basis for des Lauriers statement is that, allegedly, Abp. Lefebvre moved in a way that des Lauriers thought he must be saying the new Mass. And he also pushes the date back a year.
4. Although this concerns events alleged in 1969-1970, des Lauriers didn't mention any of this until April 1979, after he had been dismissed by the Archbishop, and shortly before he published his sedevacantist thesis.
It's rather curious to see an allegation like des Lauriers published on a supposedly Catholic site without pointing out any of the rebuttals Madiran does.