Honestly they don't say clearafy if any of them truely did died.... All they gave us was that they all been hospitalized from a tragic event..... and aren't they put into an "afterlife" a place between life and death? It seem more like they are all in a comma and they are placed in this world givng them a second chance at living their life if they want it back. In the human world they never said if Otonashi died, all we saw was him passing out from blood loss and poor health. 

Also they say Yuzuru Otonashi gave his heart to Angel so she could live again..... I but she was there a long time before he even entered that world.... (as if she was on the break of death, im a comma). I think he regain is memory when laying on her chest becuase he found his reason for living, loveing Angel. He said himself he doesn't know what he was living on for, as if he had no real reason to live and for not having a heart was the fact that he did not love anyone or anything since the lost of his little sister. After figuring out his memories and his love for Kanade Tachibana he doesn't leave like he was suppost to because she was still their, and in visversa Tachibana found a reason to live on for with the stenght of love she has for Yuzuru Otanashi. After she wanted to try to live again and left him, he came to the realization he wants to live with her and went back to earth too. They might have only reconized each other through the song Tachibana was humming (for I highly dout they really remembered what happen in the "afterlife") but the song stuck with them for it was powerful and full of life, love, and sorrow.

I think they all excepted their fate in the real world but wanted to continue living it after giving up hope thanks to Otonashi.

This is my prospective of course, but the whole reincarnation life doesn't match cuz he would have been waaaaayyyyyyyyy older then her for he "died" while she lived thanks to his heart.... and again it just shows that they could go back cuz Tachibana went back to living thanks to "his heart donation".