This is written by a theorist so they do leave the important bit out. Of course, you know just from fourier analysis the uncertainty principle. The thing is treating photons as plane waves is an approximation (a fine one for most things, particularly theoretical calculations). A better approximation is thinking of photons as wave packets that thus have some localization but not so defined as to make their bandwidth too wide (so they can be considered monochromatic).

The important thing to remember is that photons, like the very idea of a planewave is always an idealized approximation.