You are claiming that the argument commits something like the fallacy of composition with respect to the set of causes and the effect. That is to say, even if no cause has property X, it does not follow that the effect of those causes does not have property X. But like the fallacy of composition, this is not universally true. For example, if I construct a wall out of bricks that are not red, I will never produce a wall that is red.
Rational inference is another case where the fallacy does not obtain. If a set of nonrational causes come together to create some belief, that belief cannot have been rationally inferred. Rational inference requires reason, understanding, and an inferred conclusion based on the laws of logic and the premises at hand. Nonrational causes preclude such things. It cannot be the case that the statement, "It is raining outside," is fully explained by brain damage and at the same time is rationally inferred by the subject.