I don't find it that hard to swallow. Basically, your warden attacked her and she went down. You thought you killed her, but were mistaken, the warden doesn't take her pulse to check if she's dead afterward. There is NO cutscene confirming the kill as with Howe, although people have tried to insist a combat animation (beheading) as 'proof' she's dead. Call it magic, Faith, Divine interention, whatever you like, in this instance, storytelling trumped player agency. Her death occurs in a temple dedicated to a faith followed by thousands, or the walls are permeated with Lyrium, or magic and spirits/fade immediacy meant her injuries were able to be healed. Maybe she's been possessed by a spirit of Faith as Wynne had been.
There are any number of reasons she may have recovered.
People have complained "My choices aren't respected!" but really, the only choice that matters at all in the overall scheme of things is "Did your warden kill the archdemon?" Some minor things come up like "Who rules Ferelden?" "Did the warden die killing the archdemon?" But mostly the choices you made in Origins pretty much are confined to affecting Origins. DA2 reflects some of them in minor quests, but Inquisition, being even further removed from Origins' events reflects only "Who rules Ferelden from what I can tell" and even then it's a minor thing. There are some wartable missions stemming from some events/who lives etc, but otherwise, in the overall scheme of things, nothing huge.
Leliana makes mention of the "Hero" who defiled the ashes and attacked her, (with nothing good to say about him/her) but otherwise, pretty much nothing more is said about the incident. Even she is unsure how she survived the encounter, falling on her faith as an 'explanation' as to what happened.