Indeed, this conversation is a good illustration of the damage that Bayesian statistics have done to the "educated" populace. Not that they're inherently bad--it's just a different statistical approach, and it's generally good not to assume a universal background, that everything is normal, etc.--but by telling people it's fine to question statistical conclusions because the distribution might be different, it liberates certain people from ever having to actually change their minds based on new information, because they can just posit a different distribution that satisfies their own biases.
I realize this is a bit of a "no true Scotsman" but what you are talking about is a gross misuse of Bayesianism- where your own biases are incorrectly treated as extremely strong evidence.
I am partial to using unform priors over all possibilities, and then just adding in the actual evidence for which you can actually quantify its quality/strength. Your "prior" for a new situation is constructed by applying the data you already had previously to a uniform prior- not by fabricating it from whole cloth via your biases. In practice this may be impossible for humans to do in their heads, but computers certainly can!
