Twilight Bella's Lullaby song song mix up?

Before the movie came out, the song 'River Flows in You' and the song that ended up in the movie were both being considered for the film. A lot of people found the song by Yiruma better and so they thought it should have been chosen and call it the 'true Bella's Lullaby'. This confused other people who didn't know the story (like yourself).