And look at what goes into their argument: "...a wave function corresponds to
an extremal state and is therefore maximally informative
" (my bold), and "Specifically, the (necessary) assumptions are that quantum theory correctly predicts the statistics of measurement outcomes and that measurement settings can (in principle) be chosen freely." All these statements about information, they prove only things about the nature of that information. Where does that add up to reality? Completeness of information means that it isn't information any more? And just what is "complete" information? Does the wavefunction tell us what an electron is, or what its charge or mass are, or why it obeys quantum mechanics? Does it even tell us the outcome of an individual trial? Whatever they mean by "complete", it is a purely information-related definition, and statistically so.