It's no worse than a single world interpretation: These things happen all the time, the branch of math that deals with them is called Large Deviation Theory (and it's closely related to information theory).

One of the corollaries/interpretations of Sanov's theorem is that, generally speaking, when faced with an astonishingly improbable outcome (e.g. flipping 9,000 heads and 1.000 tails out of 10,000 independent coin flips), no statistical test can differentiate between "that improbable occurence with a fair coin" and "an unfair coin" - the fair coin, when it does something improbable, with have (with overwhelming probability) a specific tilted distribution that looks unfair.