You just made my case FOR me. You get all of those tones BECAUSE of how the equipment picks up the vibrations and transmits them out thru the speaker. ANYONE doing the same things will have the same tone.....simple as that. If both people use the same attack, same volume knob settings, yada yada yada then they will have the same tone. It is NOT the person making the tone, it's the equipment making the tone based on what the person is doing to it.. The person is simply changing what is going INTO the equipment....not the tone.
Of course you're right that anyone doing the _same_ things will have the same tone. The thing is, however, that usually no player, except perhaps starting ones, will play anywhere similarly, and thus have different outcomes in tone.
Is it changing the tone if you play with fingers as opposed to a metal coin? Or if you pluck the strings upwards hard as you play as opposed to strumming them?
It depends on what you mean by 'tone'. Going by the dictionary, it's not going to change that much by players.
But, if by the tone we mean the way the listener perceives the sound, well, that's mostly due to how it's played rather than equipment, of course.
There have been a few instances where I for one have been struck by how different someone sounds on same gear exactly...the first was back in late 80's when my band had a new guitarist who played thru this ancient Marshall halfstack and sounded insanely good, real Steve Vai virtuoso it seemed to us. Once I tried his rig and was totally flabbergasted...I didn't know how to effectively dampen the strings not used and also those used, so when I tried to play it, it was a mess of rattle and hum and a cacophony of sounds - the rig was VERY unforgiving indeed. And secondly, I realized the guy used next to no gain, he just really ripped at the strings and played 'em so hard it screamed...and me, I had been used to playing ultralights with a light pick and even lighter touch on a floyd-guitar. Well to sum it up - I sounded like a bad punk player on the exact same guitar and amp, and he made it sound like Steve Vai simply by playing it totally differently.
Now, arguably, the _tone_ per se was just the same...but to the listener it was a difference between ear-piercing cacophony and sweet, ringing notes.