I think the superiority will be obvious to anyone who's ever seen a few scatterplots of correlated variables, and who can imagine a graph of X against X + noise where sd(noise) = 0.1*sd(X), and who thinks for a moment. Of course many people, much of the time, won't actually think for a moment, but that's a very general problem that can strike anywhere.

Suppose the story had gone like this: Simplicio measures X, and does it so well that his measurement has a correlation of 0.6 with X. Salviati examines lots of pairs (X,Y) and finds that X and Y typically differ by about 0.1 times the s.d. of X. Then the result would have been the same as before. Would that be a reason to say "measurement is no good; use probability and statistics instead"? Of course not.