> the GHZ experiment [1] can rule out local hidden variable models and confirm QM predictions with no statistics at all
However, one needs to use statistics to even show GHZ works. That does sound contradictory to me. The correlations you get in experiments are never perfect and in this case they can be pretty far from perfect.
> one needs to use statistics to even show GHZ works
Not for the particular cases described in the quote I gave. For a complete verification of all the GHZ theorem's predictions, yes, you need to do statistics, because some of those predictions are probabilistic.
> The correlations you get in experiments are never perfect
In some cases, like the ones described in the quote I gave, it isn't a matter of correlations. You have contradictory results predicted by two different models, each prediction being 100% certain according to the model. You don't need any statistics to test that: just do one single run and see which way it comes out.
> the GHZ experiment [1] can rule out local hidden variable models and confirm QM predictions with no statistics at all
However, one needs to use statistics to even show GHZ works. That does sound contradictory to me. The correlations you get in experiments are never perfect and in this case they can be pretty far from perfect.