Without losing the generality of the theorems of probability, let me address your particular narrative: If you believe that, if a fifth column exists, it is of the type that will assuredly refrain from sabotage now in order to prepare a more devastating strike later;

This is a fancy way of saying that if you assume that the fifth column's intent is totally independent of the observance of sabotage. P(A | B ) = P(A). That is, no evidence can update your position along the lines of Bayes' theorem.

This is not what I am saying. I am saying that P(A |B) and P(A | ~B) can both be nonzero, and in the Bayesian sense this is what is meant by evidence. Either observing sabotage or failing to observe sabotage can, strictly speaking, corroborate the belief that there is a secret Fifth Column. If you make the further assumption that the actions of the Fifth Column are independent from your observations about sabotage, then yes, everything you said is correct.

My only point is that, in general, you cannot say that it is a rule of probability that A and ~A cannot both be evidence for B. You must be talking about specific assumptions involving independence for that to hold.

It also makes sense to think orthogonally about A and ~A in the following sense: if these are my only two hypotheses, then if there is any best decision, it is because under some decision rule, either A or ~A maximizes the a posteriori probability, but not both. If the posterior was equi-probable (50/50) for the hypotheses, then observing or not observing sabotage would change nothing. This could happen if you make the independence assumption above, but even if you don't, it could still happen that the priors and conditional probabilities just work out to that particular case, and there would be no optimal belief in the Bayesian sense.

For a concrete example, suppose I flip a coin and if it is Heads, I will eat a tuna sandwich with probability 3/4 and a chicken sandwich with probability 1/4, and if it is Tails I will eat a turkey sandwich with probability 3/4 and a chicken sandwich with probability 1/4. Now suppose you only get to see what sandwich I select and then must make your best guess about what the coin showed. If I select a chicken sandwich, then you would believe that either Heads or Tails could serve as evidence for this decision. Neither result would be surprising to you (i.e., neither result would change your model) if you learned of it after I selected a chicken sandwich.

In this case, both A and ~A can serve as evidence for chicken, to the tune of 1/4 in each case. A is much stronger evidence for tuna, ~A is much stronger evidence for turkey, but both, to some extent, are evidence of chicken.

I'm not disagreeing with your claim about probability theory at all. I'm just saying that we don't know that Warren made the assumption that his observations about sabotage were independent from the existence of a Fifth Column. For all we know, it was just that he had such a strong prior belief (which may or may not have been rational in itself) that there was a Fifth Column, that even after observing no sabotage, his decision rule was still in favor of belief in the Fifth Column.

It's not that he mistakenly thought that the Fifth Column would definitely act in one way or the other. It's just that both no sabotage and sabotage were, to some degree, compatible with his strong prior that there was a Fifth Column... enough so that after converting it to a posterior it didn't cause him to change his position.