Sorry, but you are all wrong (my ego). This is what really happened:
Julie was in fact the mother of Julia fathered by the publisher (note: she was talking about having her first sexual experience when she was 13 years old).
speculations:
the scar: happened in the car accident...the car accident where she supposedly died...or: a cesarian scar??...from a thirteen year old who gave birth. (I know cesarians are done differently nowadays)
the book which is given to writer by Julie:
if she really is the mother of Julia, she would be the person who has written the book...it's her own story
but: who's the woman on the photo in Julie's diary?? That's the only point where the story doesn't fit together again.
Maybe this version is useful to get closer to the real concept behind the storyline. If there is none, I don't think it's a very clever movie. Everyone can just make up unrelated scenarios and put them together to a confusing movie. To a certain extent confusion can make a movie interesting, but not when it includes major points like in swimming pools.