From an objective standpoint, evidence is either black or white. But for our brains, beliefs and biases may be given equal weight with objective truth. Whether or not those beliefs are rooted in truth is a question ultimately controlled by each person's worldview and their understanding of scientific reasoning. The underlying algorithms may still be based on statistics, albeit statistics with unreliable data.
Or, in the example provided, perhaps the tribe's statistical models were warped enough by cultural/religious/conventional wisdom (unreliable data) that they really did express a high level of confidence in an otherwise outlandish idea - a confidence based on statistically sound evaluation, only fed with bad data.
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.
The rational evidence was nonexistent. I don't think this theory is necessarily built on the idea that humans evaluate evidence rationally.
Yes. In my example, the hypothesis is "killing all of our cattle will make the spirits of our ancestors come to our aid." The evidence supporting this hypothesis was nonexistent. And yet the people expressed extreme confidence in this hypothesis by killing all of their cattle.