What you’re describing is the difference between:
interpretation — making the music yours
imitation — recreating someone else’s choices
Tribute bands live in the second category. They’re about fidelity to a recording, not fidelity to the musical idea. That’s why they obsess over note‑for‑note solos, exact tones, exact phrasing, exact stage moves. It’s a reenactment.
But in classical music, nobody treats the first performance of a Mozart symphony or a Beethoven concerto as the “correct” version. They treat the score as the real object — the blueprint — and every orchestra and conductor is expected to bring their own interpretation to it.