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A lot of the physicists will tell you that it's beyond doubt at this point, yet it seems to defy the Theory of Relativity.

You might reasonably infer it could defy classical relativity theories in a three dimensional space. But that is actually an illusion due to our inability to directly perceive higher dimensions, just as flatlanders can't perceive the third dimension. Three-dimensional space at the quantum level doesn't seem to be what we're dealing with in this universe. If electromagnetic phenomena are viewed as ripples in higher-dimensional space, and photons by implication, then the two paired photons are part of the same thing and "right next to each other" in the higher dimension. The bizarre quantum phenomena actually do start to be consistent with common sense when you consider that they occur in a greater number of dimensions.

I guess I'm not really convinced by your arguments that 1) The evidence is only statistical (that is the nature of the quantum universe); 2) We don't know what "spin" is (It is a property of objects at the quantum level -- there will never be an explanation that it is "like ice cream" or something in our macro world); or 3) That some cyclamate studies were wrong (no comment).

"that is the nature of the quantum universe..."

Well, you and I are not going to settle that here. That's what Eistein and Bohr spent years arguing about. Bohr won, according to modern physicists, but I still think Einstein was right that God does not play dice. Part of the problem with physics is that there is a degree of orthodoxy. There are some things you can't argue without being labeled a quack. That's one reason why Aristotle's view that the Earth is the center of the universe prevailed for almost 2,000 years. A lot of physicists will tell you that if you've got a theory that works in the sense that it predicts the right result, then that's all you need, even if it's wrong. They aren't going to change it until they get to a point where they just can't explain something.

Of course, some of us would say that they are already there inasmuch as they can't explain gravity. That doesn't seem to bother them though.