There's a bunch of old fights on YouTube; boxing was a popular subject for very early filmmakers. Although there's nothing representing bare-knuckle boxing per se, which had effectively been outlawed (Queensberry Rules) decades before the invention of film cameras, the style shown in these early movies was an evolution of BKB. Depending on the fighter, you can see the relatively upright stances, extended guards, etc.
I have to wonder what these old boxing matches really looked like and how they actually fought, since there's not a lot of sources being cited to back up what the guy is saying. I would think that if it were merely the open rule sets making the boxers stand in their funky, awkward looking stance, you'd see it being utilized in rule sets like sanda or kyokushin or somewhere. I just have a hard time buying anything this guys has to say without something substantial to back it up.