When I was three, SuperTed (http://en.wikipedia.org/wiki/Superted) was my imaginary friend. I wrote what I later realised was fanfiction in my head from a young age, although I didn't hear of it from an outside source until I was 16. My younger sisters often base their imaginary play on television shows, and one of them, when asked to tell me a story recently, told me fanfiction.
These are the actions of small children, who with no outside influence except the source text engaged in fanfiction or fanfic-like activities.

I don't actually write fic for consumption, because I haven't got anything like the discipline required, but yeah, I think the urge to fic is built in.