Accurate is different from identical. What you want to say is that once a performance is recorded, the music must be colored when you listen to it through some electric appliance.
My experience is that when I listen to a music, which was enjoyable through low-end earphones, becomes less appealing with a high-end so called neutral and high clarity headphone, I inevitable love less that music, because, jeez, this woman is actuall saying quite bad!
Like it is okay to add MSG in food. I may sometimes want to listen that music again with my low-end headphone.
Lots of descriptions in this forum presupposes there is the music itself. For instance, the term "colored" is not possible unless you presuppose there is one original sound. It seems that people here often have the consensus about which headphone is more neutral. But it is possible that the concept of neutral was created by the audiophiles. And there is nothing as neutral.
So, my conclusion is only about the value of originality, but share the suspicion with you that whether there is indeed something as original. This suspicion is right because listening seems to be something very subjective. Who knows your original is the same as others' original? You can be rightly skeptical about all forms of description in this forum.
But once people agree that a headphone is neutral, You are hard to disagree that there is no extra credit for neutrality.