Hi,
No Russ. I have to disagree with you. Though your explanation is partially acceptable, it is not relevant in this case.
When one is talking about the constancy of the speed of Light, he is talking about the ultimate speed of propagation of information by any means. That is the heighest attainable speed. In vacuum light travels with a speed of c, which cannot be attained by any material particle. Whereas, when light is traveling through some medium, it is traveling with a lesser speed, but still the speed limit for information propagation is c, and not the speed of light in that medium. Hence, it is possible for a material particle to have speed greater than the speed of light in the medium. The phenomenon of Cherenkov radiation is a good example of it.
A better explanation of the original querry can be given as:
Einstein's theory of relativity does not directly say anything about the speed of light. It does say that there is an ultimate limit to the speed by which information can be propagated. (i.e. the only invariant speed in the spacetime transformation is finite, unlike infinite in Newtonian relativity.)
It is an experimental fact that the speed of light in vacuum does not depend upon the frame of referrance ...so it must be invariant and hence the symbol "c" (which just denotes invariant speed of the transformation) can be successfully identified with the speed of light in vacuum.
This is nothing to do with the fact that light travels with different speeds in different media, the laws of spacetime transformation does not change with the media and hence the value of "c". It is just a coincidence that "c" and speed of light in vacuum are the same.