There's a lot of debate over the synoptic problem in the academy, but almost nobody doubts that the solution involves a literary source instead of an oral one.
Per TFA The synoptic gospels are thought to have been completed no later than 95 CE, with historical dates for the crucifixion (for those that consider the crucifixion factual) 30-33CE, placing them as no more than 65 years after the crucifixion.
Lee Strobel has a good take on the authenticity of the Gospel account in his book The Case For Christ [0] and as always the book is better than the movie
[0] https://www.goodreads.com/book/show/73186.The_Case_for_Chris...
So they have to claim that, because otherwise their claim of 'oral' tradition falls apart even harder.
However, funny enough nobody seems to quote this oral tradition as evidence anywhere. Most of the church fathers arguing with each other in the 100-150 period never bring up this oral tradition or quote from the 'Q' source or the gospels. We have plenty of text from 100-170 period but somehow the actual supposed words from Jesus himself doesn't seem to interest people very much.