Re-emission can result in extremely large refractive indices, but the weirder explanation for the refractive index is the one responsible for all the ones we experience on a regular basis. It relies on the wave property of light. If an electromagnetic wave is traveling through a medium, it will weakly jiggle the surrounding atoms, ever so slightly polarizing them. This polarization is moving charge, which creates its own electromagnetic wave. The medium’s wave will be shifted slightly in phase, causing destructive interference with the wave traveling through it and slowing the wavefront.

This explanation explains why you can have even a low-energy photon, which can’t knock an electron to its next highest energy level still be slowed.