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The main purpose of the article is to consider the following problem: Is the naturalistic explanation of the cosmic coincidences proposed by the Wheeler's version of the Many Worlds Hypothesis justified? To give the plausible answer for this question three main topics are presented. The first question concens the main issues of the Wheeler's version of the Hypothesis. They state that the Universe may have a cyclic character, oscillating ad infinitum through a sequence of expanding and contracting phases. At each 'bounce' where contraction is exchanged for expansion, the singularity may introduce a permutation in the values of the physical 'constants' of Nature and the form of the expansion dynamics. The next point of the article presents the essence of the explanation given by the Wheeler's version. of the Hypothesis. This explanation is based on the very important statement of the probability calculus that the repetition improves the chances of getting at least one rare event in a sequence of trials. The Wheeler's version offers an infinite sequence of oscillating universes with very different features so also our universe allowing life must appear at last in this sequence. The corectness of the proposed explanation is discussed in the third point of the article. It considers the problerm of the scientific and philosophical status of the Hypothesis and also some objections agaist the way of reasoning accepted in the course of explanation. In the context of the presented discussions one might say that proposed explanation of the cosmic coincidences in the frame of the Wheeler's version of the Many Worlds Hypothesis is at least dubious. Therefore, this explanation cannot be used as an argument in the controversy between naturalism and theism.