The talk about ‘residual fluctuations’ being assumed independent is pure handwaving; there is no justification for it. We aren’t even justified in calling lambda ‘fluctuations’; they are simply facts we happen not to know. Calling them ‘fluctuations’ shows you how physicists tend to think of probability expressions as ‘nature making choices’ (fluctuating) when, in fact, a probability expression can arise in perfectly deterministic, utterly predictable situations, where you simply happen not to know the details (Ideal Gas, random number generators, etc.).
Then there is this sentence, oddly written in the form of bluster: ‘‘Note well that we already incorporate in (10) a hypothesis of ‘local causality’ or ‘no action at a distance’.’’ But if you look at (10) there is nothing in there about causality at all. It is simply an expression of conditional probabilities, agnostic as to how the correlations come about. Indeed, the subject of the expression is (by my impression) epidemiological statistics, which by design have nothing directly to do with what causes people to have heart attacks. They are, at most, suggestive of where to look. To know what causes people to have heart attacks you do research into mechanisms of causation -- exactly what Bell is trying to convince you is impossible, hopeless, and not-to-be-undertaken in the field of physics.
Since Bell, the handwaving arguments have gotten more sophisticated and full of terms derived from Greek, but that is probably all that has happened.
(Postscript: Indeed, if the temperatures in Lille and Lyons are not correlated, due to shared causal factors, then I want to know the color of the sky is on your planet. Because the temperatures are correlated, it doesn’t matter whether the temperature in Lille affects the heart attack rates in Lyons; if the temperature in Lyon affects heart attack rates in Lyon, and temperatures in Lille are correlated with temperatures in Lyon, then temperatures in Lille may be correlated with heart attack rates in Lyons. This somehow escaped Bell’s notice.)