Do you believe Socrates existed? He never wrote anything down either and was essentially a lazy slob!
I have never read of any physical evidence of his existence...only in the writings of 3 authors the main one being Plato. In fact as alluded to in an early response to you thread, there is evidence he is a figure of Plato's imagination!
To my point, it doesn't really matter whether Socrates was historical or fictional. The writings don't require an historical protagonist for their meaning/value.
Like in Aesop's fables, the tortoise need not have actually won the race with the hare to understand the moral principle.