  $\psi$-epistemic interpretations of quantum theory maintain that quantum
states only represent incomplete information about the physical states of the
world. A major motivation for this view is the promise to provide a reasonable
account of state update under measurement by asserting that it is simply a
natural feature of updating incomplete statistical information. Here we
demonstrate that all known epistemic ontological models of quantum theory in
dimension $d\geq3$, including those designed to evade the conclusion of the PBR
theorem, cannot represent state update correctly. Conversely, interpretations
for which the wavefunction is real evade such restrictions despite remaining
subject to long-standing criticism regarding physical discontinuity,
indeterminism and the ambiguity of the Heisenberg cut. This revives the
possibility of a no-go theorem with no additional assumptions, and demonstrates
that what is usually thought of as a strength of epistemic interpretations may
in fact be a weakness.
