It is certainly an interesting notion that photons do not experience time, but the word 'experience' is somewhat misleading here because it implies consciousness. If we take the scientific view, the idea that photons are 'just' excitations in the electromagnetic field (which I personally think is a nice proxy to work with the wave nature of photons but basically incorrect) we can't even consider photons to be 'something', just ripples in a field, like waves on the surface of the ocean. In that case, the speed of the wave depends on the medium, the electromagnetic field in this case (whatever that might be).
If we do consider photons to be particles or 'wavicles' it is an interesting question "How do ALL photons, ALL the time keep their speed EXACTLY (within their relativistic frame of reference of course). How can a wavicle keep some fixed speed without knowing about it? The answer is simple and to be found with causality in the mind: They would travel even faster if they could - they are massless after all - but they are limited somehow. Is this by some universal 'clock' that keeps 'the time' in the universe? That's a silly notion, the universe is not some computer where all components receive the same clock frequency. The idea of the ticking of a clock being present everywhere in the universe at exactly the same moment is too silly to even consider, especially if we know that 'time' runs slower near massive objects. The whole idea of 'spacetime' is that massive objects bend it, so time is a relativistic phenomenon.
The limitation in speed that photons 'experience' must have something to do with some form of interaction, with a field or other particles, and it must have something to do with mass, since light also is slowed down and bent by massive objects, and by travelling through a medium like glass or water.
The red shift of light coming from far away galaxies proves that light coming from that galaxy is still in that 'frame of reference' for we see it red shifted. We would perceive it just as it was emitted (i.e., no redshift) if we would travel with the same speed in the same direction as the galaxy that emitted this light. How we perceive light depends on our frame of reference and so we 'experience' the frequency of light as a relativistic property.
So, do photons 'experience' time? No, they do not have a consciousness, but they are indeed limited by causality (i.e., time), otherwise they would not be limited by the interaction with mass and would not behave differently near massive objects and in a medium.
