In this longer video from Purdey's at about 59:00 the stocker explains perhaps why CNC isn't used though he doesn't say so explicitly.
They adjust the strap and locks shalpe to individual stock dimensions - that would be rather tricky with CNC I'd guess.
What is the clear liquid being applied at around the 17:18 minute mark? I know the black is either paint or ink of some sort but the clear really looks nice.
PS. Since Sam posted this video, I've probably watched it no less than 50 times. Craftsmanship like this is mesmerizing!!