I've never witnesses any of the 'Dog' episodes where he is macho. Despite your charcterization of his dress, Chapman doesn't in any way act macho and he NEVER carries a weapon. That is not someone who is 'yeller'. Nearly all of the apprehensions have been non-violent, using street informants, pursuasion and local police cooperation.
IMO he does a lot of legwork and that gets the job done, something the local gendarmes probably don't have the motivation nor resources to do.
Chapman is an idiot, wanting to be a famewhore. Its hilarious that he got busted for the same thing he busts folk for.
Bread and circuses.