Correct me if I'm wrong, but wasn't it reported that there is a deleted scene (or maybe an extended version of the cave scene) that almost made the movie where Spock prime explains to Kirk how the timeline is attempting to heal itself?
If memory serves one of the writers offered this as an explanation as to how Kirk just happens to stumble into the exact cave where Spock prime has been hiding.
I thought that I heard that the scene almost made it into the film, but was cut at the last minute. If it does exist I'm kind of surprised that it didn't make it onto the Blu-ray. In theory it could explain a lot
I think the deal was that the line to which you refer was part of an earlier version of the script, but had been removed by the time filming started. I remember that one of the writers (Orci, iirc) was quoted as saying he would have liked to have kept it in.
The explanation by Spock Prime does
figure in the novelization, if I'm not mistaken.