Not false. You don't even know what that oral teaching was.
Yes I do, it’s the same oral teaching today from an Apostolic Successor.
“In this order, and by this succession, the ecclesiastical tradition from the apostles, and the preaching of the truth, have come down to us. And this is most abundant proof that there is one and the same vivifying faith, which has been preserved in the Church from the Apostles until now, and handed in truth.” Irenaeus, Against Heresies 3,3:3 (inter A.D. 180/199).
“Then I have pointed out the truth, and shown the preaching of the Church, which the prophets proclaimed (as I have already demonstrated), but which Christ brought to perfection, and the apostles have handed down, from which the Church, receiving, and throughout all the world alone preserving them in their integrity, has transmitted them to her sons. Then also-having disposed of all questions which the heretics propose to us, and having explained the doctrine of the apostles, and clearly set forth many of those things which were said and done by the Lord in parables…that they may preserve steadfast the faith which they have received, guarded by the Church in its integrity, in order that they be in no way perverted by those who endeavor to teach them false doctrine…” Irenaeus, Against Heresies, Preface V (inter A.D. 180/199).
Catholics pass on Apostolic interpretation of Scripture, Bible aloners pass on human interpretations of scripture or come up with their own interpretations scripture, it’s all from human founders.
‘But they, safeguarding the true tradition of the blessed teaching, which comes straight from the Apostles Peter, James, John and Paul and transmitted from father to son have come down to us with the help of God to deposit in us those ancestral and apostolic seeds’ Clement of Alexandria, Stromata 1,11 (c. A.D. 205).
“The Church’s preaching has been handed down through an orderly succession from the Apostles and remains in the Church until the present. That alone is to be believed as the truth which in no way departs from ecclesiastical and apostolic tradition.” Origen, First Principles 1,2 (c. A.D. 230).
This makes sense of Paul’s words to Timothy.
“By the Holy Spirit who dwells within us, guard the good deposit entrusted to you.”
All Catholics have done is preserve and guard the Apostles same interpretation of Scripture.
Protestants handed the scriptures over to be twisted and torn apart by ravening human opinions and interpretations.
Luther’s revolutionary idea was to separate people from the ancient singular Apostles interpretation of Scripture and tell every plough boy and his dog to interpret the scriptures for themselves.
Tens of thousands of human founded churches later all conflicting on interpretation of scripture is the result. Christianity divided, Scripture nullified, truth forgotten, waters muddied.