This is indeed a very good and deep question.
Falsifiability as your secret weapon is indeed foremost a Popperian claim. One of the biggest proponents nowadays are e.g. David Deutsch (see e.g. his new book "The beginning of infinity").
Another author who tries to adapt it to a stochastic environment is Nassim Taleb ("The Black Swan"). Although when I met Nassim a few years ago in London I was especially interested in his current view on this and he grumbled (in his inimitable manner) that Popper won't work in a stochastic environment.
Anyway, trying to reconcile both views I would answer as follows: The fairness is falsifiable up to a certain lower bound. This lower bound could even be deterministic! So we are talking about a fundamental uncertainty principle. One hot candidate is the Cramér–Rao bound.
A very readable (even funny sometimes) article can be found here: http://astro.temple.edu/~powersmr/vol7no3.pdf
Generally the question also tackles the question of what randomness really is, but I won't go into this here...