> As far as I can tell, it's Bell's Theorem which shows that results we see can't be the result of hidden variables
Strictly speaking, it can't be the result of local hidden variables under the assumption that you can make decisions in the detector that are independent of the experiment that you're doing. Usually those who argue for something like hidden variables try to find wriggle room in the latter part (that these decisions are somehow inherently correlated with what's being measured). But this is also deeply weird, because you could base these decisions in principle on information that has not had a causal relationship with the experiment since the start of the universe. (this idea is called superdeterminism)
Strictly speaking, it can't be the result of local hidden variables under the assumption that you can make decisions in the detector that are independent of the experiment that you're doing. Usually those who argue for something like hidden variables try to find wriggle room in the latter part (that these decisions are somehow inherently correlated with what's being measured). But this is also deeply weird, because you could base these decisions in principle on information that has not had a causal relationship with the experiment since the start of the universe. (this idea is called superdeterminism)