The best your source can do is that there was controversy. This is somewhat at odds with your repeated declaration that there is no such thing as an Ionian mode and which you used to browbeat another poster in this thread in true Music Theory Subforum Style.fmr wrote: You can read the pages available on the Internet here: https://books.google.pt/books?id=yfFTAQ ... es&f=false
about the polemic of the introduction of the twelve modes by Zarlino, and how many composers (and even disciples, like Vincenzo Galilei) opposed to that. And we are talking about Zarlino, which has far more influence than the unknown (at the time) Glarean. Even the fourth mode was questioned, since, at the time, and because of the polyphonic practice and the "musica ficta") composers were finding it more and more the same to the third mode.
Furthermore, Zarlino based his work on Glarean - he just renamed and reordered the modes – personally, I'm not aware of anyone who disputes that. So, it's not as if putting the emphasis on Zarlino makes those troublesome modes go away.
From your source: "The history of polyphonic modality spans the five centuries from the end of the thirteenth century to well into the eighteenth. It may be divided into four stages, separated by Tinctoria's Liber de nature et proprietare tonorum (1476), Glarean's Dodecachordon (1547), and the beginning of the decline of compositional interest in the modes around 1620. The stages could be characterised as "uncertain beginnings", "general acceptance", "controversy", and "gradual disappearance"."
Furthermore, unless your argument is that zethus909 should be careful if he travels back in time to the 16th Century to practice music, the argument about who, at or shortly after the publication of the Dodecachordon, understood themselves to be composing in Ionian or Aeolian mode is irrelevant. This whole discussion began with your bald assertion that "There wasn't ever a Ionian mode, but even if it existed (outside of treaties), the fact that is had the same intervals of C Major is just a coincidence."
For that to be true, you have to work on the basis that the Dodecachordon was never published. We are not in that parallel universe.