The Jews recognizes the OT as Scripture long before it was canonized. Jesus called it Scripture and quoted from a great deal of the books in reference to Himself. His teachings validate the OT.
If that's not good enough, then nothing is.
I was making the point that amongst ancient Jews and Christians both the written and oral teachings were trusted. Not that one was superior to the other or that the presence of one suggests the absence of the other. What was important was not the method of communication but the source. In regards to the teachings of Jesus and the apostles this includes oral Tradition.
The Jews were indeed literate but the expansion of Christianity did not rely on the written word only. For an example of the place of Apostolic Tradition we have this from Irenaeus:
“As I said before, the Church, having received this preaching and this faith, although she is disseminated throughout the whole world, yet guarded it, as if she occupied but one house. She likewise believes these things just as if she had but one soul and one and the same heart; and harmoniously she proclaims them and teaches them and hands them down, as if she possessed but one mouth. For, while the languages of the world are diverse, nevertheless, the authority of the tradition is one and the same” (Against Heresies 1:10:2 [A.D. 189]).