Deuterocanonical books are part of the Septuagint Old Testament, and were therefore considered Scripture (remember +James and "all scripture is profitable..?"). When they quoted them or described events in the NT found only in them, they were quoting Scripture.
The Judaism of Christ's era was not the Judaism you are thinking of. The Essenes and the Sadducees had different theologies and considered different books as Scripture but were every bit Jewish and Hebrew.
The "Jewish Canon" you have in your Protestant Bible is the Bible of the Pharisees, not of all the Jews. It just so happens that only the Pharisees survived and morphed into rabbinical Judaism known to us today, which leads many to presume that theirs was the true Jewish Canon.
It just so happens, also, that many Jews used the Greek-language Septuagint because they were hellenized, the way American Jews read only English, because they are americanized and don't speak Hebrew.
In fact the Sadducees were the priestly class in charge of the Temple. Their canon consisted only of the five books of Moses! No Prophets and no Pslams! Threir theology was very different from the Pharisees' theology, denying resurrection and angels among other things.
And what they used did not include the deuterocanonicals. Three hundred years later the Greek Church fathers decided to add some more and that started the problems
LOL! The Septuagint was started by Jewish scholars three centuries before Christ and finished in the 2nd century BC.
The "Greek fathers" had nothing to do with what books were in it. It was a Jewish Bible translated presumably from Hebrew into Greek by the Jews, for the Jews who spoke only Greek in Alexandria.
The Church fathers included deteroncanonical books of the Septuagint because they were there all along. The fathers were also not all Greek.
Sorry. According to my historical references the deuterocanonical books were not considered inspired scripture by the Hebrew fathers at the time of Christ. If you could point me to some sources that would say otherwise I'd be happy to review the material.
As I stated before, I'm really not interested in what the Sadducees believed because they were way off base as our Lord told them. He considered the Pharisees to be knowledgable in the scriptures but legalistic in practice.
At the time of Christ, everyone knew what our Lord Christ meant when He stated, "You search the scriptures...", "What does the scriptures say...", "The scriptures states...". People didn't run around saying, "Gosh, does He mean the Sadducees' version or the Pharisee's version?