Not so.
Read Luke's intro to his Gospel.
He makes clear that he researched everything, to include sourches.
Also, why would a country full of scribes (guys who write all the time) be opposed to taking and keeping notes?
That'd be like a country full of journalists not jotting a few things down.
It was not an illiterate culture.
Is the Gospel of Mary in your Bible? How about the Gospel of Thomas or the Gospel of Judas? I wonder why not?
We know when the gospels of the New Testament were written and it wasn't till long after Christ death and ressurection.
Luke 1:2, 4
"Even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word; that thou mightest know the certainty of those things, wherein thou hast been instructed."
Instructed = word of mouth.