According to Warren Spector, it isn't the story of Epic Mickey that's important; it's how you relate to the story.

It's true. You can tell the most amazing story ever told in a video game, but it means nothing if the player doesn't connect with it. As Spector explains, Epic Mickey is the tale of two brothers - Mickey Mouse and Oswald the Lucky Rabbit - and how they reconnect. How does that matter to you, the player? That's up to you to decide.