"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.
Well, the key equation of special relativity had already been written down in 1901 as the Lorentz contraction. People just hadn't thought of interpreting it so literally.
But the larger point is still valid. Change the date to 1894 and it would be a complete novelty.
Suppose I told you that I knew for a fact that the following statements were true:
You’d think I was crazy, right?
Now suppose it were the year 1901, and you had to choose between believing those statements I have just offered, and believing statements like the following:
Based on a comment of Robin Hanson’s: “I wonder if one could describe in enough detail a fictional story of an alternative reality, a reality that our ancestors could not distinguish from the truth, in order to make it very clear how surprising the truth turned out to be.”1
1Source: http://lesswrong.com/lw/j0/making_history_available/ewg.