Once a story is out there I don't think the author's intent matters all that much. Having said this, in fanfic, there should be civility in discussions between the reader and writer. Still, the reader's interpretation has an equal validity. She can draw her own conclusions and if they do not coincide with what the writer meant, so be it. Neither is God, even if the writer is cocksure of her meaning or not so much. Particularly in fanfic, the reader brings all sorts of preconceived ideas to her reading; the characters are not entirely the writer's creation.

You mention YOU KNOW what the characters ate for breakfast even if unstated. The reader might have some ideas of their food preferences as well. But I don't think your question is about eggs vs. pancakes. It's about you as the author being right no matter what. I just don't agree. We bring our own layers and meaning into what we write (including the subconscious) and also do the same when we read. No one is God.

My own experience with my first foray into MFU fanfic involved a reader who thought my Napoleon was mean, in fact said (on a list yet) that I had written a character assassination of him. It was not my intent to be sure. Certainly I could argue my case but if that's what this reader took from my story--well-- her interpretation must have made sense for her. It really made no difference what I meant. The story stands alone like a bird pushed from its nest.