'No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.'
In this case, local hidden variables refer to what you describe as it being in a single state and us just not knowing. Without faster-than-light information transfer (which we cannot have if causality is to hold within relativity), it is not possible that 'the system is in a state and we just don't know it. '. Quoting wikipedia,
In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that a theory could not be Lorentz invariant.
This has been shown experimentally using Bell's equations and this work got him nominated for a Nobel prize but died before it was awarded that year.