Yes, I am exactly saying that many Eastern Catholics differ with the Western Church on the definition of the books of the Bible.
Trent is not binding on the Eastern Catholic Churches. The Eastern Catholic Churches are autonomous from the Western Church but in communion with it. Eastern Catholics had autonomy granted by the Thirteenth Century. Eastern Catholics ***do ***accept the primacy of Rome and the Holy Father, but are allowed to preserve traditional forms of worship (including the traditional Eastern rites and traditional Eastern definitions of the Bible).
The independence of the Eastern Catholic Churches is guaranteed by Pope Benedict 14’s
Demandatam and Pope Leo 13’s *Orientalium Dignitas. *Indeed, the Eastern Catholic Churches have their own Canon Law, called 1990
Code of Canons of the Eastern Churches.
Furthermore it is not permitted for any Latin Catholic to attempt to impose the Latin rite (which would include the definition of the Bible) on the Melkite Catholic Church. If you read Latin, you can read the encyclical
here.
Orientalium Dignitas extended this to all Eastern Catholics.
Furthermore, there is no such thing as “the Septuagint”; there is a divergence of opinion as to what books it includes – thus, the Latin, Greek (Orthodox), and Slavonic Old Testaments all claim to include the books contained in the Septuagint, but each defines that contain different books.
I realize this sounds strange, but it the Eastern Catholic Churches are a fascinating part of the Roman communion.