At last year's Bass Boot Camp (put on by Gerald Veasley), Victor Wooten was on stage taking questions from the students, and he addressed this exact same question.
His answer was that only your technique matters, and to illustrate it, he adjusted the tone controls on his bass to make it sound as pathetic as possible (cut out the bass and mids, and boosted the highs). He asked for, and received confirmation from everyone that the tone sounded terrible. Then he asked the drummer to play a beat, and he jammed to it, playing some grooves and a solo. Despite the very unconventional tone, everyone in the audience agreed that it was an awesome performance, and it still sounded great and was extremely enjoyable to listen to, because it grooved.
Then to finish the demonstration, he switched back to his normal tone and played something awkward to the same drum beat. It sounded like a beginning middle school bass player, and was completely uninteresting and uninspiring. It did not matter one bit that he had a killer tone. It was not at all pleasing to listen to.
Based on that graphic demonstration, the answer to this question is very clear to me.