Ah, that makes sense. The story did not begin at the beginning. Maybe thats the real power of the TTT. It lets you see into the past? Thats why we don't get Kellhus' POV because hes seen farther back than anyone else, not farther forward. Which makes sense a bit, because if you can see the beginning, and then follow the trance forward through the ages, you'd have far better predictive abilities than someone who is starting in the middle.
Even though the two prediction might be identical for a long time, eventually the one that started in the middle would become less accurate than the one that started at the beginning.
Its like finding an equation that describes a set of data, and then taking a subset of that data and finding another equation that describes that. Locally, both are correct, and the equation specific to that region might even be more accurate. However, once you zoom out, that equation might make no sense at all.
A straight line fits through any 2 points, but it can't accurately describe a polynomial.