Given that there is a lot of polyphony that is so obviously based upon Gregorian chant, and that is the primary type and source of polyphony, I don’t think that his argument holds water.

This seems relevant: Missa L'homme armé

Of course, Parody Masses of get a bad rap today because the word 'parody' in English as it's currently used makes one immediately think of "Weird Al" Yankovic rather than Josquin; they are also often confused with Cantus Firmus Masses (also known as Tenor Masses).

The majority of the l'Homme Arme Masses, for example, are Cantus Firmus Masses, where the borrowed monophonic song is used in one voice (the Tenor), often in long notes, while the other voices sing newly composed polyphony; though often, especially in the competitive settings of the Franco-Flemish school, highly complex canonic structures utilizing the borrowed melody are not uncommon. In addition to borrowed secular tunes, like l'Homme Arme, sacred melodies were also common, particularly votive antiphons.

Parody Masses use as the borrowed material not only a melody, but an entire polyphonic piece, often a chanson but with increasing frequency a motet (Hassler's Missa Dixit Maria is a good example of the latter.

It is also important to remember that the pre-Enlightenment & pre-Reformation Europaean mind looked at thing differently than we do today, in particular the division between sacred and secular was not as stark as today, particularly in those places with a strong cultural connexion with the theology of Calvin ... Even J.S. Bach in this regard is more at home in the company of Lassus and Josquin, as was Luther himself, than most Americans, particularly Yankees, since he not only signed his Sacred Cantatas and Missae Breves with 'S.D.G.' (Soli Deo Gloria), but also his Concerti Grossi & Clavier Suites.

It is important when looking at Parody or Tenor Masses that utilize a secular tune to look at the history, and with the allegories involved...after all, the Mediaevals loved a good allegory. L'Homme Arme, for instance, began to be used as a Mass Tenor around the time of the Crusades, and many settings, IIRC, seem to have been composed for the chapels or functions of the military orders; Also, too, the "Armed Man" was connected with Christ Himself, particularly in some of the militaristic language in Psalm 109(110), sung at vespers, particularly the 6th verse (for some reason, expunged from the LotH), and the final judgement.

There is also a very beautiful Tenor Mass by Dufay "Missa Ce la face ay pale". The borrowed monophonic song speaks of a man who is growing pale because of his great suffering in his 'love sickness'. The Mass seems to have been composed for a special Mass celebrated in honor of the Holy Shroud: In Dufay's mind, then, the 'Man with the pale face' is Christ, Who out of love for mankind, suffered and died on the Cross: literally, turning pale in His death-agony. Further, the Cantus Firmus is obscured, being surrounded by three other polyphonic voices, and also being sung at slower than usual pace (the melody is also subjected to a number of verbal canons, requiring the tune to be sung two or three times slower than notated).

These pieces are not the kind of banal imitation of 'pop' music that has plagued the Church since the 19th century, and blossomed in the post-concilliar era. These works take secular elements, and through the artistry of the composer, elevate them to the sacred realm, and set them aside for sacred purposes; much in the same way that vestment makers take the same silk fabrics used to make dresses and curtains and fashion the sacred vestments.

And what about di Lasso's Missa "Entre vous filles," based on a particularly lewd chanson by Clemens?

The origins of polyphony arise in organum, possibly as early as the eighth century. But Satan is adept at tempting people to overstep the mark, Orlando di Lasso is more than half a millennium later, and musicians are as susceptible as others.

After banishing polyphony from the Liturgy in 1322, Pope John XXII warned against the unbecoming elements of this musical innovation in his 1324 bull Docta Sanctorum Patrum. In contrast Pope Clement VI (1342-1352) indulged in it.