  The Pusey-Barrett-Rudolph theorem (PBR) claims to rule out the possibility of
a purely statistical interpretation of the quantum state under an assumption of
how to represent independent operations in any hidden variable model. We show
that PBR's assumption of independence encodes an assumption of local causality,
which is already known to conflict with the predictions of quantum theory via
Bell-type inequalities. We devise a weaker formulation of independence within a
general hidden variable model that is empirically indistinguishable from the
PBR assumption in situations where certain hidden variables are inaccessible.
Under this weaker principle we are able to construct an explicit hidden
variable model that is purely statistical and also reproduces the quantum
predictions. Our results suggest that the assumption of a purely statistical
interpretation is actually an innocent bystander in the PBR argument, rather
than the driving force behind their contradiction.
