  Bell's theorem is often said to imply that quantum mechanics violates local
causality, and that local causality cannot be restored with a hidden-variables
theory. This however is only correct if the hidden-variables theory fulfils an
assumption called Statistical Independence. Violations of Statistical
Independence are commonly interpreted as correlations between the measurement
settings and the hidden variables (which determine the measurement outcomes).
Such correlations have been discarded as ``fine-tuning'' or a ``conspiracy''.
We here point out that the common interpretation is at best physically
ambiguous and at worst incorrect. The problem with the common interpretation is
that Statistical Independence might be violated because of a non-trivial
measure in state space, a possibility we propose to call ``supermeasured''. We
use Invariant Set Theory as an example of a supermeasured theory that violates
the Statistical Independence assumption in Bell's theorem without requiring
correlations between hidden variables and measurement settings (physical
statistical independence).
