It's a literary tradition, for example every single line describing the crucifixion scene comes from psalm 22 and Amos 8. You can't prove anything came from oral tradition.If you cannot understand the implications of using the word "us", then there's no way we can go forth.
We know that the Church followed traditions as even the NT itself was composed from various oral sources. The oldest books were written decades after Jesus was crucified and were composed from an oral tradition. This is basic Christian Theology 101.
Even John's Gospel ends with this verse: John 21 But there are also many other things which Jesus did; were every one of them to be written, I suppose that the world itself could not contain the books that would be written.