In the story, Waver theories that who stablish the ritual to bring back King Arthur from the death was Morgan herself. She traveled to Wales where the cementery of Blackmore was and build the village to take care of the ritual after she was gone. Waver even thinks the statue of the Black Madonna worshipped in the village is modeled after her. But the point is she's no longer in this world (by the time of Case Files, Morgan is though to have passed away a long time ago, who knows what the new one summoned in Go is up to).
Also, all the contradiction in the stories about her are explained as the name "Morgan Le Fay" spread through Europe and become a placeholder name that assimilated many legends of fairies, witches and earth goddesses (like the ones assimilated into Black Madonnas). Like the legend of the Morrigan, that explained the three personality bit in GoA (nice reference).
Moreover, when Gray and Waver ask Kay about if the Morgan he knew would stablish such a ritual after having try a coup d'etat against Arthur and if the legend about Morgan being one of the fairies that carried King Arthur's body to Avalon while promising they return as the "one and future king" are true; he's answer is that he doesn't know because he was already death at the time but he never got to understand her. This is important because Kay's mind was used to make Add and sealed Rhon in the village.
(There is also a nice bit before that scene where Gray wonders how Kay must have felt about Morgan as both are "the brother and sister of King Arthur")