That need to adopt doubtful teachings as valid Buddhavacana would have been in early Buddhism well after the Buddha’s lifetime, not the early Buddhism when the Buddha was living as a single source of true Buddhavacana.
So the issue reported in the Sakāya Niruttiyā episode is not about the authenticity of the Buddhavacana but about how the authentic Buddhavacana was (mis)understood / (mis)interpreted by people who didnt have a background either in Buddhism or in textual/scholastic studies. There is no doubt expressed in this episode about the authenticity of the buddhavacana, but the charge against those monks is that they were spoiling/misinterpreting it through their own idiosyncratic explanations.
If the issue was first reported 100 years after the Buddha’s life so as to necessitate a vinaya rule (to be put in the Buddha’s mouth), it should still have been plausibly an issue that prevailed in the Buddha’s own lifetime. Questions about what was authentic Buddhavacana (or a vinaya rule to solve a problem that didnt exist in the Buddha’s time) wouldnt have cut it.
There is no possibility of oral transmission of a significant volume of prose texts without major changes across even one generation (leave alone multiple generations). It has no precedence anywhere in India or anywhere else. A wholesale oral transmission tradition of the whole prose sutta pitaka (as we have it today) would have meant lexical variatons in every word and every line of the whole tipitaka. You can test this - make a small speech, say 10000 words long (25 A4-sized pages) in your own language, and memorize it exactly as long and hard as you want, and try reciting it 10 times exactly as uttered by you originally and see if you get it right each time. Now extrapolate this to generations of people and to texts containing millions of words - and you begin to realize the scale of problems you get when you try to orally transmit the prose tipitaka. The lexical variants and interpolated content would keep increasing exponentially.
The prose parts of the canon (at least most of the first four Nikayas) well and truly could have come into existence only when the canon was first written down - which would be sometime slightly before or during the 3rd century BCE (the lifetime of the Mauryan emperor Ashoka). Even in the case of poetry, most of it is not from the Buddha’s time. However the earliest parts of the canon that originate from his own time (and the parts which were recited by the earliest sangha in sangiti) could have been only the early verse suttas.
I haven’t seen Abhidhamma quoting prose suttas (I dont read the Abhidhamma much) - but even if that is the case, it would only show relatively that the prose suttas were already in existence when the Abhidhamma project began - not that there were prose suttas at the same time or before the earliest known verse suttas.
Many of the elaborate prose suttas must have heavily relied on abhidhamma systematization as well, as prior to this a comprehensive early-Buddhist philosophy would not have existed. So I see a mutual interdependence between abhidhamma and the prose suttas.
The early verse suttas however stand on their own wthout dependence on abhidhamma.
But nirutti (as used in the compound janapada-nirutti, see mn139) could also mean (regional) words/expressions - this isnt an evidence of wholesale regional dialects or languages, but merely certain words being used more often than others in certain places, i.e. divergence of vocabulary by region.
Sakāya niruttiyā on the other hand, while not referring to wholesale dialects or languages either, doesnt also refer to janapada-nirutti i.e. usage of different words by region - it is talking about “their own idiosyncratic explanation/interpretation” (due to misunderstanding the original import of the Buddhavacana text).