Readers have supplied references saying that I am wrong.
Now I find a short Murray Gell-Mann interview video agreeing with me.
The Bell test experiments do show that quantum mechanics differs from certain classical theories, but not by spookiness, entanglement, or nonlocality. You could say that the particles are entangled, but classical theories show similar effects.
It is a matter of giving a dog a bad name and hanging him. (laughs) When the quantum mechanical predictions for this experiment were fully verified, I would have thought everybody would say "great!" and go home. ...That's right. The Bell paradoxes are based on comparing one branch of history to another, as if there were counterfactual definiteness. Quantum mechanics forbids this, if you are comparing noncommuting observables.
When two variables at the same time don't commute, any measurement of both of them would have to be carried out with one measurement on one branch of history, and the other measurement on the other branch of history. That's all there is to it. ... People are still mesmerized by this confusing language of nonlocality.
The Bell theorem and experiments did not really tell us anything that had not already been conventional wisdom for decades.
The bizarre thing about Bell's Theorem is that some physicists say that it is the most profound discovery in centuries, and other just shrug it off as a triviality. I do not know of any difference of opinion this wide in the whole history of science. After years of reading papers about it, I have moved to the latter camp. The theorem encapsulates why some people have conceptual troubles with quantum mechanics, but if the accept the conventional wisdom of 1930, then it has nothing interesting.