Since I am big on splitting grammatical hairs, I would say that your fingers create style or character. But even then you get into some murky territory. A person with a very specific playing style, like Geddy Lee for instance, would sound mostly like Geddy Lee no matter what. Although the sound of him playing YYZ on a P bass with flats would probably elicit a few "What is that guys problem?" comments. However, there are a lot of session players that can imitate the playing styles of other known players, or play to have as little "character" as possible. The idea of bass players having an immutable "finger print" to their playing is a little bit of a myth, IMO.IMHO the axiom means: Regardless of what bass and gear you use, you will always sound like you. It doesn't necessarily mean your tone will be exactly the same though.
IMHO, to a large degree your fingers (actually the way you use your fingers) do create tone, but the pickups, amp, speakers, strings, and even to a small degree the wood and scale of the instrument tend to take this tone and modify it substantially.
To me the word "Tone" means sound. Yes, how hard and where the player plays a string will absolutely impact the tone created. That said, no bass player on the planet with make a P with flats sound like a Warwick Thumb with SS round wounds. The laws of physics make it impossible. You fingers will never make an SS 12" 100w combo amp sound like an SVT-CL with an 810, which will never sound like my Mesa Subway D800 and Barefaced Super Twin 212 cab. Again, physics.