What does it mean for a story to write itself?
For me, it's as if I've read journals, a long time ago, that were written by the characters on their journeys. I'm racking my brain to try and remember all of the entries I've read, and even though I have a good, long term memory, I'm still finding it difficult to remember exactly what I've "read." Some entries are easier to remember than others, and some, I remember what was done, but not the exact words. I remember details of other passages at random times, so I have to go back and fill those in. I often find myself having to fill in details, thoughts and feelings by myself, so that's fairly hard, but when I think about the character and the situation they're in, I can guess what that character might do, think, or say.
This way of thinking makes the story and characters seem like they're actually breathing things, living a "normal" everyday life. If my characters and stories are mistaken for being non-fiction, then I don't necessarily see that as a bad thing. No matter how "fiction" it is, when telling a story of events, everything should be real.
In short, the stories I write are not my own, they belong to the characters within them.