Does light always travel at *c* even when moving through a medium?

The title of the question is a bit misleading, but with limited space it was all I could think of. So, I know that light travels at fractions of c when traveling through a medium; however, as I understand it, the reason for this is because the photons will be absorbed then re-emitted a short period of time later. My question is do the photons travel at c once the atom that absorbed them spits them back out, or do they travel a reduced speed in between their atom absorptions? For example, let's pretend we can track a single photon through a light year of water using an internal tracker on the photon that tells us when the photon "exists," i.e. it's traveling as a photon, and when it "doesn't exist," i.e. it is temporarily absorbed by atom and has yet to be emitted. Let's assume the photon that is absorbed and then emitted by the atom has the aforementioned tracker, regardless if it is the same photon. Now, that tracker is attached to a stationary clock. When the photon "exists," the clock runs, when the photon "does not exist," the clock stops. So, if we were to clock the time it took the photon to travel through the water, basically ignoring the time spent absorbed by the atoms, would it travel the light year in one year? Also, would all photons take the same amount of time? I suppose the fundamental question here is exactly what is it that causes light to slow through a medium. I am assuming the absorbing and emitting by atoms is not the only thing that slows light as I have read some articles where light is slowed to 38 miles per hour (http://news.harvard.edu/gazette/1999/02.18/light.html), and if it was light being absorbed, then the light would be held up in the atoms for the VAST majority of the time spent traveling through the medium.