Thea…true and false. Believe it or not, both you and the
'Gator are right.
Your first paragraph is close to on target. However: the Hebrew Bible included only the books in the Protestant Old Testament (“protocanonicals”) – and there was some debate on which of the “Writings” were canonical. The Septuagint
included a greater range of books, including Wisdom and Apocalyptic material that was used more or less devotionally by Jews of the Diaspora. Jamnia merely ratified the common use of Palestinian Jews, to restrict what they considered Scripture to those works known at the time in Hebrew. Supposed authorship by a historic figure (Moses, Samuel, David, Solomon) was also a major criterion. (Ecclesiasticus was written in Hebrew, and Hebrew manuscripts have survived, but was not known to the Palestinian Jews, since it was an Alexandrian product.)
There was debate down through the history of the church as to the validity of the deuterocanonical scriptures (those in the Septuagint but not the Hebrew Bible). Jerome, who translated the Vulgate and was the leading Bible scholar of his day, was opposed to their inclusion in the Canon. However, these were not seen as critical disagreements, but simply difference of opinion over non-essentials, before the Reformation.
Trent did formally set the canon for the Roman Catholic Church as the wider canon founded on the Septuagint. This was done in reaction against Calvin, Luther and Zwingli’s insistence on the narrower Hebrew canon. It was seen more as “spelling out what we’ve always practiced” than as innovative, but the fact does remain that it was at Trent that the canon was officially defined for the RCC.
For me and us Anglicans, it’s very much a tempest in a teapot. We found doctrinal teachings exclusively on the narrower canon, and have occasion to use material from the wider one as appropriate. I find the deuterocanonicals mostly to be on a par with the least useful parts of the protocanonicals, and don’t see a whole lot of reason to argue the point.