The GHZ/Mermin experiment refined the Bell argument into an "all-or-nothing" experiment with three parties. In that scenario, there are no probabilistic tests. Alice, Bob and Charlie each receive one particle (entangled, of course) and make a local decision to measure one of two quantities of that particle: x or y, each with a binary outcome. The decision to measure x or y is local and beyond the light cone of influence of each.
No matter what they chose to measure, the results are strongly correlated. So much so, that it is clear that you cannot predict every outcome of what the three parties measure. There just isn't a single pre-determined logically consistent assignment of outcomes before the actual measurement (there is a parity restriction of the outcomes).
But the measurements are consistent anyway. So, either there is faster-than-light communication which enforces the consistency, or indeed the outcomes cannot be decided until one of them measures something. It just isn't mathematically possible.
This is also independent of the physical theory by the way. You don't need Schroedinger, Dirac, or anything. Any physical theory that predicts measurements just like QM would will have this restriction. So hidden variables are incompatible with locality (no faster-than-light communication).