A universal constant is generally one of those numbers that we assume is the same at any point in the universe. Important numbers such as
pi,
e,
gravitation,
the speed of light in a vaccuum, charge on an
electron, value of human
life (that last one is still under debate...).
I say we assume that these numbers are constant everywhere. Certainly bad things would happen if we walked into an area where pi=4.5 and our blood vessels all decided to expand to meet the new requirement for circle circumference. And if light came to a dead stop in a vaccuum somewhere, there would need to be a damn good explanation -- probably prohibative to continued sentience. And if human life ever became devalued, well, then we might just live on Earth as we know it today. And that would be tragic.
So, we continue blithly along, assuming universal constants and trusting to my physics professors teaching: "This is all assuming the laws of physics do not change over time... an unproven assumption."