I'd not seen fanfic in that way before, but that is so true. We are writing original stories, even the characters are our own to some extent. We can get them to do anything we want - sometimes out of character, or maybe not - people do strange things in different circumstances, and none of us is predictable all the time. Even the most famous authors, writing original material, are influenced by others.
Not all of us are Shakespeare, few of us will even be officially published, but all of us has something to say, something to contribute. Long live fanfic!