For me, in a work of fiction, the story has a life of its own. It exists as an independent entity, more of a found object than a composed one; an excavation rather than a creation. Now, that doesn't mean I'm against editing and revision - changes to help a story realize its potential are, to extend the archaeological metaphor, removing the dust and debris. (Literary criticism is the scientific paper discussing the find. Fanfiction is ... all right, I'm taking the metaphor too far now.)
When I refer to story here, I want to clarify that I don't just mean the plot: I mean the sum total of character, world, plot, and to a lesser extent, tone and mood. Since I primarily write secondary world fantasy, the analogy is easy for me: the story is the history of another world. I debated a bit whether to include those last two, but decided that there's a sense of mood and tone in "real life," too, so it's appropriate to consider that part of the story.
There are other elements that may exist in a work of fiction that are intertwined with story, but (in my mind) separate from it: theme and message; education; raising awareness and increasing diversity; filling a niche; style and language; narrative structure. Some people would argue that it is impossible to separate message from story, and in the end, I agree. Even if the author doesn't consciously intend to say something, he or she does: even if it's, "sometimes, life is random."
Beautiful prose; intriguing facts that give the story life; how could I be against any of this? I'm not. I can hardly rail against experimental narratives when I've written not one, but two stories in first person plural ("we"), another entirely as a dialogue between two minds trapped in a single body with no outside cues, and am currently submitting a tale with two different endings - which completely change the context of the tale before.
But for me, there's an important caveat: these other elements must grow out of and/or serve the story, not the other way around. The story is always first. It's about authorial intent: I need this element to tell this tale properly. When a story because slave to other elements, because a writer wants to send a specific message or deliberately write something "wacky," the story begins to gasp for air. It loses verisimilitude. The long-buried pottery begins to crack.
Obviously, though, defining when this happens is very subjective. Unless the author has been interviewed about the writing process for that tale - and possibly not even then - it's nearly impossible to know in what order the elements were conceived, where the inspiration started. A story I find ridiculously contrived might seem perfectly natural to someone else, and vice versa. And, of course, we all have blinders: favorite elements or pet peeves that blind us to "flaws" or highlight them with a spotlight.
So it goes with every work of fiction: taste is subjective. One thing comes out of this that is immutable, though: for me, personally, whenever I sit down to write, I concentrate on the story and chisel out everything else from there.
Real archaeology makes me sneeze.