From the Doctor's point of view: there's a lot of memory erasures and aborted timelines going on.

From River's point of view: she knows that the first Doctor she can meet and that can actually remember that meeting is 10 (because "her" Doctor told her), and she knows how to work around that - again, memory erasures, or working behind the scenes to help the Doctor's previous incarnations. In Silence in the Library, River means that that's the youngest she has ever seen the Tenth Doctor, and it's the first (and only) time she's met a Tenth Doctor that didn't already know her, which made her realize that that was their first proper meeting from his POV - the one she wasn't supposed to somehow erase.