(please note that this is my first post)

I found the phrasing in terms of evidence to be somewhat confusing in this case. I think there is some equivocating on "rationality" here and that is the root of the problem.

For P=NP, (if it or its inverse is provable) a perfect Bayesian machine will (dis)prove it eventually. This is an absolute rationality; straight rational information processing without any heuristics or biases or anything. In this sense it is "irrational" to not be able to (dis)prove P=NP ever.

But in the sense of "is this a worthwhile application of my bounded resources" rationality, for most people the answer is no. One can reasonably expect a human claiming to be "rational" to be able to correctly solve one-in-a-million-illness, but not to have (or even be able to) go through the process of solving P=NP. In terms of fulfillingone's utility function, solving P=NP given your processing power is most likely not the most fulfilling choice (except for some computer scientists).

So we can say this person is taking the best trade-off between accuracy and work for P=NP because it requires a large amount of work, but not for one-in-a-million-illness because learning Bayes rule is very little work.