This argument and explanation is constantly coming up on the subreddit askscience. I don't violently oppose it as much as some do, since I think it's somewhat helpful, but I would like to say that my preferred interpretation is that a `photon' isn't really a well defined object when inside strongly-coupled materials. For example, can you really sensibly talk about a freely propagating radio wave when its still within a quarter wavelength of an antenna? When atoms are spaced tenths of a nanometre apart and visible light has a wavelength of hundreds of nanometres it seems a bit silly to talk about it propagating freely in a material.

When you go through quantum field theory, photons are defined in terms of freely propagating particles, not interacting with other fields. When the disturbance in the EM field propagates into, e.g. a dielectric material, and strongly couples to various nuclear and electronic excitations, it is better described in terms of a massive quasiparticle, the polariton, which is a hybrid of the photon, phonon and electron fields and, being massive, propagates at less than c. You can, of course, describe it in terms of perturbations to the free photon corresponding to various types of virtual absorption and re-emission, but it's a bit misleading to think of it being physically absorbed and re-emitted with little stopovers. If anything, the classical model of a continuously interacting medium interacting with the EM wave creating a coherent response wave which interferes with and appears to slow down the EM wave is more instructive.