  In a recent paper (arXiv:1111.3328), Pusey, Barrett and Rudolph claim to
prove that statistical interpretations of quantum mechanics do not work. In
fact, their proof assumes that all statistical interpretations must be based on
hidden variable realism. Effectively, the authors demand from the start that
reality must be decided by mathematics, and not by measurements. If this
unjustified assumption is dropped, the quantum formalism has a natural
statistical interpretation that fully explains the paradox presented by the
authors. It is therefore possible to conclude that the paradox actually
supports the statistical interpretation, demonstrating once more that quantum
mechanics should not be explained by measurement independent realities that are
never observed and therefore lie beyond the reach of empirical tests.
