From the "ask Bear" chat on Discovery's web site:
stealther: What do you have to say to people who claim you used a flotation vest instead of your backpack when you rode down the river in your previous show?
Bear: That was the first show I did, and health and safety insisted if I wanted to get in that river with those rapids, I had to wear a thin flotation device for one particular shot. After that show, I told the producers if I'm going to do it, I need to do it on my terms, i.e. no vest. And the rest of the series, they've allowed me to do it all my way.