I suggest you take a look at this list of physical constants, paying special attention to the "uncertainty" column, and then get back to us on why you don't accept any of them except the speed of light.
That's an absurd statement. For example, planck's constant is known to better than 1%, as is the mass of various particles. Heck, the Earth, which is sufficiently non-spherical for it to matter only differs in radius (between polar and equatorial) by 0.3%!
G (the gravitational constant) is an interesting one: the value is only known to about 5 significant figures, but GM (the gravitational constant multiplied by the mass of the Earth) is known a lot more accurately, unsurprisingly, considering how well GPS works. Some of those constants seem to be known to about 12 significant figures.
