There is that idea yes, that there was an oral tradition for fifty years until the author of Mark came along. It is also possible the Mark Gospel was two lost written accounts that were merged, meaning the oral tradition was much shorter. About 85% of Matthew is found in Mark and most of the 15% are Greek legends. Luke seems to have had Matthew, Josphius, and Mark. John seems to have had the three plus that weird community that might have existed in Jerusalem. I hate using weasel words but really this is all speculation. Not convinced the M source had to have existed, since you can get there without it.

It is worth mentioning that the story about the adulteress in John was in oral form for a long time before written down. So, yes it is possible that this feat happened more than once. Pity that story is even less likely to have happened compared to the rest of the stories, given how nice it is.