Extreme indeed, the former anyway. I've seen this a couple of times but those people didn't necessarily "trust their senses above even well-calibrated instrumentation", at least they didn't put it that way.
Instead they just say or imply there's
a) something supernatural going on (you can always blame it on supernatural but using the supernatural is a non-explanation), or
b) the measurements are missing something that would explain the "heard" differences (I guess people would still use this point even if the measurements are complete), or
c) a mix of both, or
d) they just dismiss measurements or science for whatever weird reasons, so all they are left with are purely subjective experiences, getting sucked into the audiophile downward spiral of wasting money.
Anyway, what they tend to overlook is that you don't need your eyes to hear differences that are actually there, just like you don't need your ears to see differences in color.