I think you're using a definition of 'evidence' that is too narrow or perhaps too logical, although I agree with pretty much everything you're saying.

I think that the statistical theory is possible but certainly couldn't be objective (one big reason being the cognitive biases you mentioned). Meaning a person will do the necessary mental gymnastics to assign the necessary value to the variable 'evidence' that their brain uses.

In your example, I think some combination of religious belief, regret avoidance, and herd thinking all added up to equal the requisite 'evidence' needed to express confidence in the cattle killing hypothesis.