Georgina Woodward
You remain unclear on the concept. The results are not being compared to a theory prediction, they are being compared to a theorem prediction; a theorem (Bell's theorem) that has been proven to be true. There is, as you say, some probability that a mere theory may be false. But there is no possibility whatsoever, that a proven theorem may be false. So the only remaining question is, is that proven theorem, even relevant to the actual, physical problem?
For example, there is no doubt that the Pythagorean theorem is correct, but is it even relevant to the problem of determining the distance to be traveled, between two points, when the travel path between those two points, turns out to be something other than a straight line?
Even if you have a proven "Magic rabbit theorem", it is not going to yield a lot of correct predictions about what might come out of a "Magic fruit hat", that only produces a random selection of fruits, rather than rabbits. The rabbit theorem is not wrong, but it is irrelevant. Instead of "testing" Bell's Theorem, physicists should be testing quantum results against Shannon's Theorem, not Bell's theorem; because Shannon's is the relevant theorem, if you ever hope to understand quantum phenomenon.
Just as the Pythagorean theorem will not yield accurate distance predictions for non-straight paths, Bell's theorem will not yield accurate correlation predictions for non-identical particles; but Shannon's theorem does.