Note that your own source is more or less not a rebuttal, certainly not enough to call the 'PBR' an "imaginary fact". From it I would draw the following conclusions instead:

0. It is a Letter To The Editor in a scientific journal, rather than a paper. I believe that such letters are typically less thoroughly peer reviewed, which the tone of language used also supports.

1. "Paoletti herself never endorsed the PBR in her own articles and book"

2. she made the weaker claim that the gender coding of pink and blue was inconsistent —not reversed— at the beginning of the twentieth century and that the current pink-blue convention only became dominant in the 1950s

3. That we may not be able to establish any political motivations behind some quotes used to support PBR/inconsistency

4. That an automated review of a corpus of literature from 1800 to present for /a very specific form of wording/ may indicate that Pink and Blue historically over this period had the current meaning

That final point is the weakest. Searching for a specific phrase would always carry with it a risk of excluding related phrases that are hard to automatically include. Languages change over time as well, so this may mean that the phrases themselves gained new meaning. There is also the question of the items that make up the caucus - do they accurately represent the popular culture of their publish date? And any given book may not have same weight in the culture of the time as any other.

But perhaps more worryingly, the letter states the caucus consisted of over 5 million books. Yet the percentages that are then used, eg 0.000003%, are completely and utterly meaningless for any caucus under roughly 35 million (if I've got the maths right).