Michael Kruger qualifies the notion that the Apostolic Fathers depended primarily on oral tradition and highlights some indicators of the importance of written texts to them. He summarizes,
There’s little doubt that oral tradition still played a role in the second century and beyond. But, the evidence above suggests that there’s little reason to prefer oral tradition as the default, catch-all explanation for the Gospel tradition in the Apostolic Fathers.
On the contrary, the “bookish” nature of early Christianity, and its deep textual identity, suggests that we should be open to the idea that these authors—at least sometimes—knew and used written Gospel texts.
For the balance of Kruger’s discussion, see his original post.