If the artist actually declares their intention, does that count for anything?
Tolkien is the one who's correct, right?
About what he intended, yes.
About what his story actually means, no. I wouldn't limit that to what Tolkien insists about it.
I have a policy of telling my students never to explicitly trust the author when they state either intent or lack thereof. It's not a question of "The Death of the Author," it's a question of creatives in the language arts being notoriously... shall we say inconstant?... when it comes to their creative motivations.
For instance, Lord Byron outright stated at times that he wrote the great Epic Satire,
Don Juan, to piss off Bob Southey.
Or at times because he needed the money. Or because he was inspired by, and wanted to pay homage to,
Orlando Furioso. Or because of political questions of Greek independence. Or even a few times because he was bored. He would tell friends that he had an overarching moralistic plan for
Juan, then mere days later claim he was making the whole thing up from whole cloth and was completely directionless.
And every time he changed his story, he explicitly stated that the previous reason he gave played no part in his creative process.
And Byron's not alone in this. Most every author who has ever denied an intent or claimed one has contradicted themselves in print or their personal correspondence at some point or another, be it Matthew Arnold, Virginia Woolf, Mark Twain, or Terry Pratchett.
I can, off the top of my head, think of one exception to this, and that's Heinlein. He was remarkably consistent about why he wrote various works. But even him I wouldn't necessarily trust.
EDIT: That's not to say that when an author connects a work to an explicit idea or event in the real world, it should be disregarded. Obviously,
1984 is a book about some very real, very much identifiable people, events, and philosophies in Orwell's world.
But it is best to take it with a grain of salt when Orwell, or P.B. Shelley, or Stephanie Meyers tell you what you "need to know" about their work.
I know men who have made tracing the real intent of a single author for a single 10 line poem their lives' work - and they will not succeed in their lifetimes. Despite the author explicitly claiming his intent in the notes to that poem.