Hmm...

I should have paid more attention in Physics class when they talked about Michelson-Morley and Einstein's work (that whole relativity thing)... But wasn't that the whole basis of the thought that light needs no medium to propagate?

If I understand right, the old school of thought before relativity was that light needs an an all-pervading "ether" (even in empty space) to propagate, and by extension the speed of light would change if the speed of the source changes. The Michelson-Morley experiment showed that lightspeed is constant no matter what the speed of the observer or the source is, which lead relativists to conclude light needs no medium to propagate.
Shee-oot, all these concepts are so fuzzy I should have read that book by the wheelchair guy. :-) :-)