Authenticity of Mahayana

In the notes for Unit 1, Prof Terentyev states that "It cannot be established... that Saykamuni Buddha taught in only one or all of these Indian languages", referring to Pali, Magadhi and Sanskrit.

Here a transcript of a recent article in Tricycle that supports this position.
The article is entitled "Whose Buddhism is the Truest" and its position is based on the discovery of the Gandharan manuscripts.

The conclusion drawn by Prof. Salomon, a scholar overseeing the translation, is that there is no verifiable basis for the belief in an original, singular, pristine canon.

The author states:

"Every school of Buddhism stakes its authority, and indeed its very identity, on its historical connection to this original first canon. Buddhists of all traditions have imagined that our texts tumble from the First Council into our own hands whole and complete—pristine—unshaped by human agency in their journey through time. This sense of the past is deeply ingrained and compelling. If our texts don’t faithfully preserve the actual words of the Buddha in this way, we might think, how could they be reliable? Isn’t that what we base our faith on?"

and:

"As scholars scrutinized the Gandhari texts, however, they saw that history didn’t work that way at all, Salomon said. It was a mistake to assume that the foundation of Buddhist textual tradition was singular, that if you followed the genealogical branches back far enough into the past they would eventually converge. Traced back in time, the genealogical branches diverged and intertwined in such complex relationships that the model of a tree broke down completely. The picture looked more like a tangled bush, he reported."

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Dharmakirti

The notes for Unit 1 also provide Dharmakirti's "two decisive criteria for authenticity of a Buddhist text."

1. Only those themes that repeatedly appear throughout his teachings indicate what Buddha actually intended.... A text is an authentic
Buddhist teaching if it accords with these major themes.
2. The correct implementation of its instructions by qualified practitioners must bring about the same results as Buddha as repeatedly indicated elsewhere.

With all deference to the Nalanda-educated Dharmakirti, if these are indeed his "decisive criteria" they appear to me to present substantially logical flaws.

1. Any text that is written on a common theme could become accepted based on this criterion. Furthermore, a substantial number of apocryphal texts written on an established subject, each also referencing a previously unmentioned concept, practice, view etc. could then establish that new point as appearing repeatedly.
2. There is a problem here of validation. If I say the practice yielded the same results, how would another verify? If I thought I had brought about the same results, how would I know?

Simply pointing to the re-occurrence of themes from the Pali canon in the tantras and stating that the masters have had realizations by following these tantras does not disallow the possibility of fraudulent texts being introduced under these criteria.

The question of authenticity, what I perceive as a flawed set of criteria could perhaps even form the basis for the counter claim of inauthenticity, with the foregoing being regarded as a ruse to validate non-original material and include it as canonical and Buddha-vacana.

If there is a point I am missing regarding this particular point in defense of the authenticity of the tantras, I'd be most interested.

Regards