In electrostatics, it's often claimed that we can assume the electric field inside a conductor is zero. The way I interpret this claim is:
If we have a region containing charge which can move around freely, then the only situations in which no charge is moving are situations in which the electric field is zero inside the region.
The reasoning is that if $E$ were non-zero at some point, then the charge at that point would start moving. But what if there's no charge at that point? It seems to me that the only thing we can really say is that the support of $E$ and the support of the charge density are disjoint.
Is this not correct?