And note that the effect is not inherently quantum mechanical-- the index of refraction of materials can be understood classically, the primary requirement is an understanding of complex numbers (and most of those advances came with quantum mechanics!). The classical description is related to the response you get from a harmonic oscillator if you drive it at a frequency away from its resonance frequency-- the amplitude of the response is less the farther from the resonance you are. There is also a phase shift that comes from the interaction, so the amplitude of the response controls how much out-of-phase interference you have to add in when you do the "superposition" of all the things the light is doing. The higher the amplitude of the interfering terms, the more the light is slowed.

Quantum mechanically, you can frame the amplitude of the response in terms of the probability that the photon will interact with that atom. So I'm not sure where the uncertainty principle per se comes into play (in some sense it is hiding behind all quantum phenomena, that is true), because I wouldn't necessarily characterize the issue as how long the atom holds the photon, because the phase shift far from resonance is always pi/2, and a fixed phase shift will act like a fixed "residence time". Instead, what changes with frequency is the amplitude, or likelihood, that the atom will be involved in slowing the photon's progress. I'd like to understand the connection between these two descriptions of the frequency dependence.