You have to make the assumption that there is this oral tradition, because without it your whole system collapses. But you have yet to demonstrate that this oral tradition existed and that it communicates something other than what we have in the Scriptures. Well, thank you for admitting that you can't come up with a Scripture verse that teaches what your thesis requires you to. I, for my part, would be happy to come up with all kinds of Scripture verses which indicate that there are things that are authoritatively transmitted in non-written form. The concept of Moses' seat is not taught in Scripture, and yet Jesus considers it binding on these consciences of his listeners.
Oral tradition is capable of transmitting something without inscripturation.
I told you about these things. He does not explain it in I Thessalonians, he does not explain it here, but he expects them to understand and to take heed and to take warning based on oral tradition. These are many examples of Jesus and the Apostles practicing what Catholics practice, that oral tradition can provide a normative transmission of truths that we should incorporate into our system of belief even though they are not contained in the canonical written group of Scriptures. Jesus doesn't assess the legitimacy of the Scribes' functions but questions the way they exercise them. You then reference such things as the rock in the wilderness.