It's not justified for any rigorous setting at all.

In a layperson setting, it's as justified as saying the speed of light slows down in non-vacuum. It doesn't, but it's a close enough explanation for most people most of the time, and if you squint it's sort of saying the right thing, but missing all of the details. In the same way as the observed speed of light is slower in air, the tides happen every 12 hours. But c doesn't change and there aren't two bulges.

It 100% does not, every single photon is moving at the full c speed of light at all times. It's not even that the photons are bouncing around and so they, on average do not make progress as fast. I believe it's a factor of how the moving EM field of the photon nudges particles like electrons a little, whose now moving field results in a lower net wave phase velocity such that observed propagation time is < c, but every photon still moves at exactly c.