“You can actually give a semi-plausible justification of special relativity based on what was known in 1901.”
You can give a semi-plausible justification for anything. It was obvious at the time that our knowledge was incomplete, but the specific way in which our knowledge was incomplete was still a mystery. It is very easy to invent a plausible-sounding quack theory of physics; that is why we have the Crackpot Index.
“So I found this counterexample, and saw that my attempted disproof was false, along with my dreams of fame and glory.”
I know how that feels. When I was 14 or so, I took a course on cryptography, and the textbook proclaimed that modular inverses were the basis of public-key algorithms like RSA. I felt that modular inverses were crackable, and I plodded along on the problem for a few weeks, until I finally discovered a polynomial-time algorithms for doing modular inverses. It turned out that I had reinvented Euclid’s algorithm, and the textbook authors were idiots.