I didn't see that Show, but I first met Cody at a gathering hosted by Bounder Outdoor Survival School. Cody had been with BOSS before starting his own school. He was barefoot when I met him. I have never seen him in shoes once in over fifteen years, and that includes snow, although he will concede to socks in deep snow. The bottoms of his feet look like leather.
He has always, since I have known him, walked the way you describe. I asked him why. He said it had to do with being conscious of each step. Cody walks his own path, but as a former survival school instructor and a guy who's had his feet in the dirt for over 60 years, I can tell you that he knows whereof he speaks.