but... but... that's precisely what is supposed to be happening according to the currently accepted models: the red shift is _not_ due to the galaxies actually moving apart in space, it is due to the space itself expanding between them, in combination with the fact that the speed of light remains constant despite the expanding space.
Now, if space is expanding, then I could hold one end of a (long enough) yardstick standing on this galaxy, and you could hold the other end standing on another galaxy, despite the red shift, because the yardstick would be expanding together with the space between the galaxies. This essentially means that there is no way to detect the expansion of space in the physical world other than by studying light. Which means that if light behaves in some way that we do not yet understand, then it could very well be that there is no expansion taking place at all.
The tired light hypothesis says forget that awfully exotic stuff about expansion of space, there is a much simpler explanation, everything is more or less stationary, nothing is expanding, and the red shift is due to some as of yet unknown property of light which reduces its frequency as it travels through space.