Like other areas in physics the resolution of EM/light phenomena can be described at many different levels and when you try to combine the terminology or equations from different levels, you usually end up confused :)
Like <PERSON> implies, the simple phase-equation that relates a pathlength to a phase depends on an assumption of a wave propagating with a fixed speed and a fixed wavelength. Except for polarization, this is enough to describe the propagation of light in a classical way.
However in more general descriptions, a Lagrangian formulation is used where the concept of a wave itself doesn't really arise until the equations are extremalized. That is, if you write out the "path integral" as a sum of the $exp(iS/\hbar)$ contributions where each $$S=-\int L dx^4$$ as you've probably seen in the textbooks (<PERSON> example above with the EM field tensor F is the kinetic part of the EM Lagrangian), you see that you do the integral over spacetime (the L here is the Lagrangian, not the pathlength). 795
The Lagrangian formulation is designed so that the extremal value of this corresponds to the usual wave-propagations, but you actually formally sum over any configuration of the spacetime field in question.
Also, in a flash of confusing circularity, the photon propagator you've read about which is used to perturbatively find solutions to the above, is actually just a <PERSON>'s function of the already extremalized solution of the free photon field per the above general formulation.. I wish I could dig deeper into this here but I'm just learning how these different formulations fit together myself. Suffice to say, if you want to build a completely particle-based approach from scratch, you need to postulate the shape of the propagator.
As <PERSON> notes in his simple QED book he makes a couple of shortcuts. Apart from leaving out polarization, after talking about the simple path-length-dependent phase in 10 chapters he then casually drops the note that this is simply an approximation and tries to explain the framework of the above in 2 pages, much to the confusion of the reader :) 682