Regarding your “long game of telephone” comparison ... let me refer you to this website: http://coldcasechristianity.com/
You may want to start with this video, which shows that the “chain of custody” is a matter worthy of serious consideration:
http://coldcasechristianity.com/2014/the-importance-of-the-new-testament-chain-of-custody/
It is, of course, nothing like a ‘game of telephone’.
It’s much more like a college course; material is written down for anyone to read, and acknowledged experts relay further explanations that they learned from their teachers, and the material is discussed and debated openly. Those who best master the material then become teachers themselves and are granted status and emulated. Someone who misrepresents the texts or the lectures is challenged by others with the same background.
Nothing at all like a hurried secret conversation such as in the game of telephone.