If a 30-06 is fine in B then so would a shotgun with slugs.
A shotgun is probably the most versatile firearm ever made.
You can take anything from birds to bears, re-load it fast, hold 7-9 rounds and normally they can take a beating and keep on working too.
A 30-06 while fine for big game would never let you take a bird or a rabbit for that matter... at least not with any meat left worth eating.
It's hard to tell from the picture as I haven't seen the show but it looks like an 870 to me. I have an 870 and love it. For in the woods for protection, and general hunting I would go with an 870 20" barrel and mag extension. Smooth barrel, with shot ranging from 00 to bird, slug and a handful of hard cast slugs. Load the mag minus one and at any time you can make your second shot or pump out the first and make your first shot whatever you want.
If we are talking only protection in grizzly country then minimum 44mag... this guy went into the woods to "live". Look at people in the olden days who were on horses and lived in the woods they had pistols on themselves a rifle on their horse and sometimes a shotgun. He wasn't in my opinion over loaded, but he sure as heck didn't need all those things to "survive".
Bear country warrants a pistol of some sort, and for food gathering a .22LR is good. Add a shotgun and you can take down big game at further distances EASIER than your pistol or birds (not that you can't take a bird with a 22 though.)
Anyway... I can see how he thought he'd wanted all those fire arms they are all useful for different tasks but crossover a lot too