Right, discussed many times before. The consensus is that he is from an alternate Royal line (I think via Camoran Usurper). The common knowledge was that only a Septim can wear the Amulet, but this may be incorrect. In the game, like in real life, not every thing your hear or read is true. And that may be because it was not common knowledge that another Royal blood line existed.
(It could also have just been an oversight by the developers)
He did wear it though, you see him wearing it as he enters into his own paradise.
Right, you can see that he is wearing the Amulet in the Dagon's Shrine quest.