You are absolutely correct. From http://dsc.discovery.com/fansites/manvswild/chat/transcript_06.html:

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.

I?m not expressing an opinion in any way, as I already have elsewhere on this board, but I just wanted to point out the facts.