via relativity, "perceived time" is elastic - a-la Lorentz contraction etc. but modern physics is still done under the assumption that there is an universal "standard clock" which an observer in an inertial frame could reference with a constant speed of light. that the speed of light in a vacuum is constant, has always been constant, and always will be constant is a fundamental assumption for all physics.
only in the very small (quantum) and the very large (cosmology) is that assumption ever really important. as far as i know, there isn't a coherent theory of a micro or macro scale that allows the passage of time to fluctuate - the value for c is a "standard candle" for the passage of time, so any theory that allows for (reference - not observed) c to vary is effectually one in which time itself varies. for example hyperinflation cosmology relaxes other physical assumptions, to account for a perceived expansion, but doesn't assume the universal time clock "slowed down" to allow the universe to stretch the perceived amount in the perceived time-frame. instead it supposes space itself was able to defy limits imposed by c.
the thing about "elasticity of time" as a conception is that time doesn't "exist" -- it's a measurement not based in any physical medium - it's still a little sketchy if a photon is a 'physical' thing or not, but that's not quite what i mean - time isn't a thing that is observed, but a measuring stick by which observations are made. at least in the way (most) physics treats it, though you may have a different view.
how would you differentiate between a second being slightly longer or shorter, and the speed of light being slightly slower or faster? or between either of those and space itself stretching or contracting, causing a (constant speed) photon to travel a longer or shorter distance? commonly accepted physics discards the idea that the measuring stick could change length, assumes the photon in the absence of other forces does not change speed, and measures such an effect (not the perceived effect in a relativistic sense, but any absolute difference) as expansion.