If you can, in reality, hear it in a controlled double blind test, that counts as a measurement. There is nothing that says a measurement has to be done with a mechanical device. But you need, no matter what, to be able to provide statistically meaningful results from a properly controlled experiment. As the aphorism goes - the plural of anecdote is not data.
This debate has gone on for decades. It is always the same story. Nothing changes. Indeed what is claimed in terms of sonic signatures for various resistors could have come verbatim from a conversation on rec.audio.high-end 25 years ago. I remember back then Vishay buk foil resistors as being the source of the sound of 80's HiFi. The same replies are still current. People fool themselves. You can't usefully tinker with an audio circuit and gain the experience unless you adopt a serious level of experimental discipline. ABX testing isn't a difficult regime to set up, but somehow tinkerers never seem to be prepared to go that last little bit.
But we do have measurement capability and sufficient understanding of the human audio system that together can provide an ironclad guarantee that some changes cannot, under any circumstances, be detected by ear. However there are no end of audio enthusiasts that prefer a coloured sound.
There are arguments about accuracy. Does it measure accurate or sound more like music? That is not a valid question, something that is often not appreciated. We know, a-priori that it isn't possible to capture and reproduce an acoustic with even the finest equipment possible. Everything you hear in your reproduction is a mix of engineering and aesthetic trade-offs. No doubt - some recordings don't sound all that great, and in your particular system, with your taste in sound expectations and experience, you may find some additional colouration makes the music come alive for you. Where this breaks down is that it is useless to assert that these particular colourations are the best, or will be preferred by others. There is however one simple common ground. No colouration. It may actually sound worse. But it is a common ground.
We know how to make amplifiers with provably no sonic colouration. They are neither complex or expensive by audiophile standards. Hypex, PuriFi, Douglas Self's designs, Neurochrome come to mind. There are others. But there remain a slew of deliberately coloured amplifier brands. We have seen a few here. They have a house sound (well some do). Some will admit to deliberate euphonious tweaks in the design. (AKSA for instance.) Some mumble about fairy dust. Trouble here is that ascribing to one specific component the sonic signature is very difficult. Once a design has been perturbed, there are many interacting aspects that come into play. Commonly these designs start with a low global feedback design. Then lots of competing effects come into play. Some parts of the circuit may act to counter distortions in another, and linearising that part may actually make things worse. Unless one has a detailed circuit model and can also measure things, one will have no idea what is going on.
