I think I correctly assume this Buddhism site is (appropriately) open to many, if not all, forms of Buddhism(?) However, when folks say things like “Buddha said” I often wonder what to make of this. Are there recommended well-researched references materials (hopefully, with relatively little ax-to-grind) to help with appreciating the validity of such statements?
They're probably referring to (but not necessarily quoting from) buddha-vacana.
As for recommended references -- English (or other European) translations of Pali Canon
I can't tell you about references to Mahayana literature.
The abstract states:
This work articulates and defends a single thesis: that the Early Buddhist Texts originated in the lifetime of the Buddha or a little later, because they were, in the main, spoken by the Buddha and his contemporary disciples. This is the most simple, natural, and reasonable explanation for the evidence.
Our argument covers two main areas:
- The grounds for distinguishing the Early Buddhist Texts (EBTs) from later Buddhist literature;
- The evidence that the EBTs stem from close to the Buddha’s lifetime, and that they were generally spoken by the historical Buddha.
Most academic scholars of Early Buddhism cautiously affirm that it is possible that the EBTs contain some authentic sayings of the Buddha. We contend that this drastically understates the evidence. A sympathetic assessment of relevant evidence shows that it is very likely that the bulk of the sayings in the EBTs that are attributed to the Buddha were actually spoken by him. It is very unlikely that most of these sayings are inauthentic.
Please also see this answer.
The truth is real arising and real vanishing relative suffering, trillion times per second. Another only left truth is Nibbana.
What can let people get in those both is "Buddha say" no matter from whoever.
However, normally people who can get in and keep "Buddha say" is the Jhana Mastery who memorize entire Tipitaka an other pali canon in Pali form.
The other else is individual which hard to prove their skill especially by the ordinary.
For me as an ordinary person who memorize some Sutta in pali, I normally advice either beginner or the older to go to meditate with Jhana Mastery who memorize entire Tipitaka instead of randomly reading by themselves.
It's because after I got in Tipitaka, I realized It's impossible for no-Jhana-person to read them all without confuse and misunderstood. Even I try to describe people by quoting the Sutta Pali directly whether how these all cannons are not conflict each other, they still quote them all to conflict each other instead because many reader has no Jhana, so they have no eyes to see what is really arising and what is only imagination.
Even a little misunderstood in Tipitaka could make the reader waste this entire special life to practice follow the Buddha. Why? Ariyuppavada and Cetokhila (Blaming the noble one and wrong decision of the noble one who Memorized Pali cannon through 2600 years).