People are interpreting the question in different ways.
There are a lot of artist who are highly distinctive and always recognizable not because of their tone, but because of their phrasing, their rhythm, their overall approach to improvisation. I would put Monk, Cecil Taylor, Charlie Parker, and John Coltrane in that category, for example. Not that Bird and Trane didn't have great individual tone. But I would say that their genius lay elsewhere. Other artists like Ayler, Bechet, Webster, Pres, Getz, Hodges, Lockjaw et al hit you right away with tone alone. That was a huge part of the whole package.