Is it just me, or is Naoi's death linked to the scene where he finally gets his father's approval? I mean, when he and his brother fall, they're underneath a tree with a broken branch, which suggests that they were climbing the tree and fell. Remember that the only time Ayato ever got his father's approval is when the two twins were climbing the tree and he grabbed the fruit before his brother did.
Is it possible that Ayato wanted to keep climbing taller and taller trees to win his father's approval and eventually he and his brother fell, causing his twin's death? It would definitely tie into his guilt over his brother's death.