Tone is in the brain, perceived through the ears and is a culmination of 2 components:
Gear
Technique
The interaction of these two components, yields a final result which are interdependent on each other, to produce a signal that is passed through the air, to the ears and processed in the brain equaling tone, for the listener.
It is NOT one or the other because great gear doesn't guarantee great playing or great tone, AND great playing doesn't guarantee great tone, and poor playing doesn't guarantee bad tone (just bad playing)
I think a great player, playing on crappy sounding gear, will sound like a great player with crappy sounding gear. It's really not any more complicated than that.
The same great player, playing on GREAT sounding gear, will sound like a GREAT player with great sounding gear.
Same for a crappy player playing on GREAT sounding gear. They'll sound like a crappy player playing on great sounding gear, though, they'll NOT likely have the gear sounding as great as it could. :idea:
* Tone is in the brain, via the ears, NOT in the fingers, though finger picking vs a pick does sound different
* Technique is in the fingers, and will help one coax nuances out of equipment
While a seasoned player is just that, a seasoned player, their tone IS dependent on their gear. If you don't believe me and think that their tone is in their fingers, ask them to get a Flanger tone without plugging in their electric guitar, or get feedback, or delay tones, higher gain etc... or have them while playing unplugged, change the tone of their unplugged Les Paul, Tele or Strat sound like a Dobro or an acoustic guitar preferably a Gibson J200, or have them make a steel string acoustic sound like a ukulele, or a classical nylon string.

It ain't gonna happen
I think the reason most seasoned guys sound like themselves, no matter what they play through, is because they tend to dial in the sound they prefer, no matter what they play on, AND their touch on the instrument (technique) is uniquely theirs. I think a given player playing through a clean tone, will tend to dial in particular characteristics, as close as they can, to their favorite clean tone vice versa with a distortion tone.
I've noticed that most seasoned players will play appropriately for the tone/gear the ARE using, rather than trying to dial in a tone that the gear that they are using was NEVER designed to produce in the first place. (They are not likely to, while plugging straight in to a Fender Twin, going to try and play brutal death metal riffs, nor are they likely to while playing through a high gain amp set to do high gain likely to play Stairway to Heaven or ballad type of clean stuff.
Otherwise, THD and every other amp manufacturer wouldn't have more than one model or design because no matter what, a given player would sound the same through every piece of gear. (They don't) Gear has characteristics, and if tone weren't from the gear- a Pignose would sound just as good as a THD, An EHX Holy Grail would sound the same as a Lexicon PCM-80, etc... etc... They don't
my $.02