Was the Fizeau experiment independent of the refractive index of the medium?

The Fizeau experiment happened before Michelson-Morley, and Michelson-Morley was so important because it cleared up the ambiguity in Fizeau's result. Fizeau's experiment was designed to help Fresnel's drag theory, and it looked like Fizeau had supported it. Fresnel's drag theory was used to explain Arago's experiment, which in 1818 showed the earth was in the center and not moving. Fresnel came along and tried to win the day back for the heliocentrists by saying the reason Arago's telescope gave that result was that an ether out there dragged the light and distorted the image. Then, eleven years after Fizeau, George Biddell Airy did his experiment in 1871 using two telescopes instead of two light beams through the same tubes, and he found again, as Arago did, that the earth was not moving. After that they went to the Michelson-Morley experiment in 1881, and then the more precise 1887 version, where they set the apparatus in a mercury bath to absorb the vibrations, because it was so sensitive it could feel people walking a hundred yards away. They made it a hundred times more precise than it needed to be, and again found the earth was not moving and called it a null result. So Fizeau was one small part of a whole sequence of thought the scientists were developing in the 1800s: Fizeau, then Fresnel, then Airy, then Michelson-Morley.