Noncontextuality as a meaning of classicality in Quantum Darwinism

Quantum Darwinism proposes that the proliferation of redundant information plays a major role in the emergence of objectivity out of the quantum world. Is this kind of objectivity necessarily classical? We show that, if one takes Spekkens' notion of noncontextuality as the notion of classicality and the approach of Brandao, Piani and Horodecki to quantum Darwinism, the answer to the above question is `yes'.