Computers can measure to arbitrary precision, so that's not the problem, and if you have good reason to think that you have 25 sigmas worth of evidence, that's

Computers can measure to arbitrary precision, so that's not the problem, and if you have good reason to think that you have 25 sigmas worth of evidence, that's still very different from a religious belief which needs infinitely more evidence to justify, or a religious belief of having unshakable meta-belief in the probabilistic model such that you never update it when it's wrong. The problem is really just a bad model, or (as with Challenger) ignoring the computer/engineer/model completely. Probability is in the mind; "events" happen, not "25-sigma events"; if your model is predicting a very low chance of something that happens much more than warranted, your model is very wrong. Is it so wrong it needs to be cast out entirely? Possibly. I'm more interested in how it gets updated when it's wrong.