I have seen countless examples where Gauss' law is applied to state that the electric field in a region is zero. For example, taking any Gaussian surface inside a spherically conducting shell where there are no charges inside, we find the the surface integral is zero by Gauss' law, but then it is always claimed that this implies the electric field is zero. Why is this the case?
Couldn't it be that there is a uniform electric field through the Gaussian surface such that the total surface integral comes out as zero but individual sections of the surface will have a non-zero field value?