It didn't claim to predict the list very well. Its purpose is to give intuition about how far around the Earth we can see.

Also it shows that simply being tall (airplanes go higher than Everest) doesn't get you on the list. The second paragraph puts an upper bound on sight lines between two mountains of a given size. The longest sight lines are pretty close to that limit. And it gives a simple experiment that anyone can carry out from an airplane which will let you see the curvature of the Earth.