Heaviside wrote: And the Tipitika was written down some four or five centuries after the Buddha's death. So what is the "real" authority? I don't think the arguments of Pali scholars help a lot given the provenance of the Tipitika itself.
Re your question on provenance, I can think of 3 fairly reliable dating methods that work with texts rather than manuscripts or inscriptions.
For one, practically all of the sources in the early Buddhist schools regard the 2nd Council as having taken place about either 100 years or 110 years AB. Only the Mahasanghika source does not give the timeframe. On this basis, those suttas and sutras which can find parallels in the Mahasanghika canon can be assured of an early date. Post-schism, the schools were no longer of speaking terms and it's unlikely that the Mahasanghikas kept up with Nikaya and Agama developments. Those shared suttas/sutras can therefore be said to have closed no later than 100 years AB.
Secondly, we can use the dating of the various Abhidharma material as an indication of when the suttas/sutras more or less "closed". There are exceptions to this , of course, but as a general rule of thumb, we can certainly see that the large bulk of the suttas pre-date the Abhidharma. And there are fairly good estimates of the dates of the various Abhidharmas.
Lastly, when you consider how geographically distant schools share so much parallel material, a very reasonable explanation must be that the parallels attest to an early shared heritage before the schools migrated from the common centre. If you link the dispersion to Asoka, then you again have an event that could not have happened more than 230 years AB (depending on which chronology you use).