Actually, I believe that's exactly what it means. At least when it comes to fretboard wood, which I consider the least important indicator of how a bass is going to sound.Every single time isn't going to happen - each piece of wood is different. But that doesn't mean that the woods in question don't have certain tendencies.
I prefer to say it's how the subtleties of the bass player influences the bass.As for being able to tell one from the other on recordings, you might as well ask people to consistently identify what is a Precision and what is a Jazz. Most wouldn't be able to do that, but that doesn't mean there isn't a difference between the two. And it isn't only a matter of what is heard "out there" - it's also a matter of how the subtleties of a bass' sound influences the player.