Ethan,
Everything that matters with audio is well known and can be measured to orders of magnitude beyond what any human can hear. For example, all types of distortion can be measured down into the noise as low as -120 dB and even lower.
The human ear is much more sensitive than you think. There is a lot that is NOT so well known or accepted and plenty of things that are easily discernable by the ear that are not so easy to measure. Your example is just talking about amplitude there is way more to it than that.
Most people are hard pressed to hear artifacts that are 40 dB below the music except in special situations.
How about spacial cues? Why does one pre-amp allow for a deep sound stage and then another one jumbles the sound stage up in a 2 dimensional way. The ear detects it quickly and easily. To measure it takes some doing to determine not only what to measure but how to measure it and what component is contributing to the problem.
Likewise for frequency response which can be measured to tiny fractions of a dB at frequencies from well below what anyone can hear into the radio frequency range. So what else is there?
My Clio measuring system can very accurately measure the amplitude of a note, but it won't tell me what played it. In fact I can make two different instruments play the same note and look exactly the same on a measured frequency response, but they very sound different.
Too often we try to quantify the sound of something by a handful of commonly accepted parameters. These commonly accepted parameters will let you know if there is a problem before you even hear it, but it won't tell you how good or bad something sounds. Good or bad is a subjective evaluation too. Two things might measure the same by common means yet sound very different. It could be that the root of the difference lies elsewhere and you are measuring the wrong thing.
This is my big objection to the snake oil merchants. They know their products do nothing, so they instead claim the improvement is real but "science" doesn't know how to measure it. Every real audio engineer knows this is silly.
There are clearly snake oil merchants out there. The subject of this thread when it started points out a really good one. Most "real" audio engineers know that if it measures good but sounds bad it is still bad.
Case in point just hand me a bunch of Radio Shack drivers and I can put enough components on them to make them measure great in every way, but that does not mean that they'll sound good.
Another case in point. A manufacturer hands me two capacitors to evaluate and compare wanting my feedback. This really happened. They are the exact same value and measure the same in every way, but the dielectric material is different. Guess what, they sound different too.