Uhm, I assumed that because you
said he didn't know about the theory of relativity.
The fact that c = constant is widely accepted to be one of its postulates. If you don't believe me, then see wikipedia.
The Principle of Invariant Light Speed – "... light is always propagated in empty space with a definite velocity [speed] c which is independent of the state of motion of the emitting body." (from the preface).[2] That is, light in vacuum propagates with the speed c (a fixed constant, independent of direction) in at least one system of inertial coordinates (the "stationary system"), regardless of the state of motion of the light source.
Yes, the Maxwell-equations are not invariant under Galilei-transformations, and they provide very strong evidence for why this postulate is a good idea.
Still, going that one step further and realizing that this is actually a fundamental part of nature is what we usually consider a genius move. Something Einstein himself did. Not something just anyone would do.
Setting c=constant and then not doing the rest of special relativity is some sort of "mish-mash" of classical mechanics and the theory of relativity. Sometimes, this mix will provide good results, and sometimes it won't - which can be said for every mix of "correct and wrong" theories to various degrees.
