Well, the narrator doesn't really "know" anything--it's an author's construct, nyet? If we envision the narrator as a character--and I'm not sure we inevitably do that with omniscient--then we'd probably envision her as existing after the events of the novel, like we do with a first-person narrator, so there'd be no precognition necessary.

After all, even if it is from River's point of view, there's still a narrator in some sense, as its told in third person, and the narrator "knows" what River is thinking, but it'd be odd to say the narrator is psychic.