I can't believe how little discussion I've seen on this, and that it never occurred to me before. I only found one small old thread on reddit, with a couple poor arguments in it. Here is the evidence as I see it:
1. The story is told from Red's perspective as narrator, meaning every ounce of it came from Andy and how he chose to portray himself to his cell mates.
Andy's story in court was that he went to confront his wife, armed, motivated, and drunk, he dropped bullets with his fingerprints everywhere, then he changed his mind and left. His gun then vanished mysteriously, never to be found. As a spectacular, trillion-to-one coincidence, his wife was murdered by someone else that exact same night.
2. The story Tommy tells about Elmo blatch admitting to killing in a similar manner to that which happened to Andy's wife really could be inaccurate or a coincidence, exactly as the warden said. It's certainly far more likely than Andy's ridiculous defense being true.
3. Andy was a rich man convicted by a jury as guilty beyond a reasonable doubt. That doesn't just happen easily, even in those days.
4. The original novella leaves his innocence more ambiguous (e.g. the warden doesn't kill Tommy), so it's possible the movie simply slanted things to appeal to the widest audience, making Andy a hero.
