Why so much faith in meters and so little trust in human hearing?
Because it is known - without a shadow of a doubt - that human hearing is unreliable: It's subject to perceptive biases. Our unconscious brain literally changes the information coming from the ear before our conscious brain "hears" it. If it didn't we would be unable to function.
I have tinnitus. No physician would insist that I don't--yet it can't be measured and science doesn't know what causes it. Does that mean it doesn't exist?
Exactly - most likely your tinnitus (like mine) is a function primarily of your brain, responding to faulty (or lack of) signalling from the ear due to hearing loss or damage. There is no signal reaching your ear that creates your tinnitus. Your tinnitus only demonstrates the fallibility of the auditory system, not its acuity. You hear stuff that is not there.
Detail (read or ignore - up to you):
one of the aspects of being human is having a brain that acts as a prediction machine. All those optical illusions you’ve seen, or the auditory illusions you've heard : They're the result of your brain making stuff up from imperfect senses bringing in imperfect information.
See that 3D world all around you as you look around? That perception exists only in your brain. It is built from the ground up based on two tiny blurry and with a blind spot right in the middle images projected onto your retina. I think it is almost miraculous how the brain manages to create that perception for you.
Now without moving your head, picture the stuff that is behind you. You can actually build that into your perception of the world even when not looking at it. It is not coming from any of your senses - it is simply a prediction from your brain based on what you've seen in the past.
Ever been walking down a path in woodland and seen a person up ahead that turns into (e.g.) a tree stump when you get closer - that's your brain predicting.
Ever heard someone say something, and then they deny they've even opened their mouth - brain prediction.
This is happening all the time. Our brain is continuously making pretty good predictions based on imperfect information - we couldn't function if it didn't. Sometimes though it gets the predictions wrong. And it is multi-sensory. It can alter sound based on what you see, or change what you see based on what you hear. Or how we feel, or what we've imbibed, or how comfortable we are, or if we are in unfamiliar surroundings.
It is well known that we will hear differences between audio devices even when there is no difference in the sound reaching our ears. We've all experienced it. In fact we all experience it all the time. Ever sat down to listen to music to find your system doesn't impress you the way it normally does - or on this day it suddenly sounds sublime. The system hasn't changed, you have : your perceptions have.
Your subjective listening can be evidence, but it has to be controlled (eg accurately level matched) and blind (so that you don't know what device is playing), and you have to be able to consistently detect the difference (at least 9 out of 10 times). With this control we can be certain that your biases are not influencing the result.
Without that level of rigour, then your subjective experience is nothing more than anecdote and tells us nothing about what actual physical differences there may (or may not) have been.