"...It seems probable that most of the grand underlying principles [of physics] have been firmly established and that further advances are to be sought chiefly in the rigorous application of these principles to all the phenomena which come under our notice. It is here that the science of measurement shows its importance — where quantitative work is more to be desired than qualitative work. An eminent physicist remarked that the future truths of physical science are to be looked for in the sixth place of decimals."

Note that quote is from 7 years after his experiment. Michelson did not believe his own result! The idea that he was discovered was correct, was so utterly weird and difficult to understand, that the possibility of it being true simply did not even occur to him, or most of anybody for that matter! He actually thought that his failure to measure the speed of light was related to instrumentation or precision, and he would repeatedly pursue various efforts to try to correct his mistake, which was not a mistake at all!

Basically he showed that (from the perspective of the time) 2+2=5. Naturally he rejected this without even really considering it, while Einstein not only accepted that it might be true, but then spent years working out an explanation for why! Had Einstein been wrong, it would have looked like the odd behavior of a man battling with his sanity, even more so given that much of his key research came while he was working as a patent inspector, no university of the time being willing to take him on as staff!