Actually here is a real world example to "disprove" that theory.
A few years back we saw The Moody Blues. It just so happens we were in third row right in front of John Lodge. He played a Fender Jazz Bass. His tone was exceptional (to me). Sadly about 2/3 into the set he broke a string. They swapped him out with what looked to me like an exact same Fender Jazz bass (and why not). From that moment on no matter what he did the tone was "S H ! T E". I'll assume both basses were strung with the same brand and age of strings (or maybe not).
So not even two "exact" models sound the same, why would a Gibson Bass (known for it distortive qualities) sound like a '50 Fender P-Bass etc. etc. etc.?