There is quite a bit of fret noise in most recorded bass tracks. Fret noise, fret buzz, clickety clank, its all there in a lot of tracks. It just disappears whenever it is played in a mix. You notice it because you are basically playing straight into a headset. Chuck probably used flatwound strings, although I'm no CR expert so don't quote me. Flats have very reduced finger noise compared to rounds.
You can hear all kinds of fret buzz in these tracks for example:
You can hear all kinds of fret buzz in these tracks for example: