I think that we're seeing River Song post Silence in the Library. She's been brought back from the Library's virtual world, and her personality has been put into a clone or android body. My feeling is android, because she seemed a bit too relaxed about dropping into space near the start, but I'm probably wrong.
Now, an obvious objection to this is that the crash is referenced in River's "where are we in our timelines?" remarks in SitL, but this is where wibbly wobbly timey wimey come in - for some reason the timeline has shifted so that River wasn't there when she was needed, and the Church has brought her back from the dead to patch this hole.
I'm probably wrong, but it makes a certain amount of sense in Whovian terms, and if clones / androids have some sort of stigma it would explain the Bishop's remark about the Doctor not knowing what she is.
Anyone got any better ideas?