yeppers, of course "relative" being the key meaning to that presumption.
So, that observation holds true when velocity is not a factor, and I am standing still next to you...or not moving very fast, or moving at the same speed you are. We, at that point, would all be considered moving at the speed of light relative to one another, and time is not a factor.
But in terms of traveling from point A to point B (over distance and when velocity matters) light in the relavistic world is 186,000 per sec. And, hypothetically, as you approach C, let's say you're in a ship and your twin brother is still on earth...time on your watch...though seemingly still ticking away the minutes, time is ticking away far slower then the watch on your brothers arm as he stands back on earth (motionless compared to you). Thus, relative to your brother you are now moving through time as well as traveling over a distance. (Typical analogy)
Thus, time is relative and the speed of light constant.
Yet light slows when traveling through matter as density increases.