I have just last week visited a talk held by mr. mcbride.
He said that he didn't like pickups, using only a microphone normally and if using a pickup it is only to give more body, not for altering the natural sound (as if this is not what pickups are supposed to do, well).
During the talk he played without amplification in a pretty big hall. And it sounded just the same: a *big* sustained tone; and it wasn't even his own bass he was playing …
They did 'Body and Soul' with a local pianist and the singer who didn't contribute too much, but the bass was all way in the center: timing, harmony, melody just by a few notes played at the right moment with a perfect attitude.
Later on he said: "you, as the bassist, must know the song better than anybody else"
So it seems true what they use to say: "all in the fingers" ;-)
I asked him how to achieve that quality of sound & playing. He answered: "oh, you now, just a lot of playing". He was recalling jams in philadelphia when, after 12 chorusses of horns at 220, someone shouted: "now: bass solo" and he said: "oh, no"
But then, after seeing the YTclip again (out of synch), you could say that Bob_the_bassist is right; there is certainly some compression going on, at some point in the chain ...