The other side of the debate would be that if the mirror is moving towards or away from the light, the reflection will be Doppler-shifted to a higher or lower frequency. Does this mean that the reflected photons are not the same photons as the incident photons, or does it mean that the same photons have had their energy changed? I think there is no meaningful distinction because every two particles with the same name in quantum mechanics are identical anyway. There's no telling which are which. If I showed you a photon, then took it back and showed you another, you would never be able to tell whether I had opened the same box twice or if I had taken the old one out and captured a new one from my desk lamp.