The f-stop is not changing, which is the ratio stays the same. Constant aperture is really constant f-ratio., which means effective or virtual ratio. A truly manual constant aperture lens operates differently than by-the-wire lenses, which is why the older ones are so large, they have to maintain that ratio over their range. Newer lenses do it differently which is why they are referred to as having virtual constant ratios.
Btw, that Canon approach is pretty limited. Try that trick on a wterfall and you will see the waterfall change from falling water to shaving cream.
These discussions may convince you otherwise:
These have been problems for a while, and folks are trying novel techniques to fix them.