Is that bad? If you're turning AC into DC you're gonna have to rectify it somehow.
Then at 3:55 he gets shocked from touching those same terminals (as he should), with the circuit disconnected from the AC line, to segue into the need to discharge capacitors. This is what makes me question how much of his "getting hurt" is actually acting.
(Also just in case anyone is watching those videos and thinks there's a distinction between his usual haphazard behavior and when he gives explicit "safety" advice - there isn't).
In this case I'd guess he's got some decent calluses and any leakage current isn't going through any nerves. Also he's only touching it lightly so won't be making very good contact.