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Masanes, Galley and M\"uller [1] argue that the measurement postulates ofnon-relativistic quantum mechanics follow from the structural postulatestogether with an assumption they call the "possibility of state estimation".Their argument also relies on what they term a "theory-independentcharacterization of measurements for single and multipartite systems". Werefute their conclusion, giving explicit examples of non-quantum measurementand state update rules that satisfy all their assumptions. We also show thattheir "possibility of state estimation" assumption is neither necessary norsufficient to ensure a sensible notion of state estimation within a theorywhose states are described by the quantum formalism. We further show theirpurportedly "theory-independent" characterization assumes several properties ofquantum measurements that exclude plausible alternative types of measurement.We illustrate all these points with specific alternative measurement postulatesand post-measurement state update rules. We conclude that, contrary to somefolklore, quantum mechanics is by no means an island in theory-space. It canconsistently be extended by rules for obtaining information about quantumstates other than via POVMs. Whether such rules are realised in nature, forexample in linking quantum theory and gravity, is an empirical question thatcannot be resolved by theoretical analysis alone.

The measurement postulates of quantum mechanics are not redundant