Interesting question. Let me reply by asking how would one go about finding an answer to this question? One could do lots of experiments here on earth, but then one might ask how things are acting on the other side of our galaxy? Or one can look out at all the other galaxies using telescopes and see how things are working there. But since it took light a long time to travel from those galaxies, what were are seeing is from a long time ago. Perhaps something has changed since then.
So the short answer is that there will always be some uncertainty about blanket statements about the speed of light being constant in ALL locations in the universe. It would make sense that it is the same everywhere and for all time, but short of a pronouncement from the Creator, we won't know for sure.
But so far, all our measurements have showed that the speed of light is constant in all frames of reference.
Now I'll add another wrinkle. Speed is a RATIO. It is distance per time. And it is the variance of time flow that makes the speed seem constant in all frames of motion. That is why a man who speeds away on a rocket for 1 yr out and 1 yr back will find that he is ever so slightly younger than those that stayed home on earth.
Stephen Wolfram is working on a theory of
cellular automata, where the universe is composed of tiny parts that interact with each other. He calls this a "graph", but I like to think of it like pixels in the
Conway's Game of Life. Each part or cell or pixel just interacts with its neighbors, following pre-set rules. It is the vast sea of these elements that comprise the quantum fields, which in turn, carry the energy of the electromagnetic fields which we perceive to be light. And in an interview on YouTube (I can't find the link right now), Wolfram described that it seems that each automata seems to allow motion (moving energy along the grid), OR time flow, or some ratio of the two. Thus the faster something is passed from node to node, the slower time will progress for that entity. What is time flow? It is the working of the laws of physics that allows a clock to tick, or a radioactive atom to decay.
My point with all this is to say, that if there was a pocket in the universe where the action of the universal grid was slower, then both changes in distance, AND changes in time could be affected. And thus the ratio (the speed) would appear the same to observers existing in that grid.
tl;dr -- the speed of light is constant, but there is likely a deeper reason for that.
KT