If we see fanfic as "the reworking of another author's characters" then this form really only appears for the first time in history with the invention of legal authorship in the 18th century through copyright and intellectual property laws, after the invention of the printing press.
Er.
Greek drama? (a lot of which probably counts as 'Homer fanfic', no, by this definition?)
Even Shakespeare, did not own the stories in his plays. A patron would commission him to retell a story and he was paid in royalties.
Somehow this does not accord with my assumptions about the economics of writing for the theatre in the Jacobethan period... Plus, is there not a more interesting tale to be told about dramatists of that period riffing off other people's revenge tragedies, mashing up diverse elements (shine on, Cymbeline, that crazy diamond): see also, Restoration drama. (Oh gosh, and John Dennis and stealing his thunder!)
We think Mr Morrison (o dear, just look at his moody young man photo at the head of that article) is missing so many points that my Naked Hedgehog icon would probably be appropriate. Like, just how much story-telling is picking up stuff that's already there and reworking it and giving it a different spin and adding in something else.
Pretty much everything derives from something.