The way I understand it, and I could be wrong, Hunting can take place at any time by a member of the tribe, which isn't something that can just be bestowed upon anyone. Hunting would come in under provincial law, and would be possible, the bow season should be pretty long. Then its just a matter of the guys having the right license, which for a non-resident might be pretty expensive. There might also be a restriction regarding needing a guide, but I don't know for sure, easy to look up, can't be bothered.
For the purposes of the filming, my suspicion is that any animal killed in self defense would be treated as it is normally, in that you don't get to keep the hide, (although you would have to turn it in at some point, probably when you are done sleeping on it) a bear that was hunted becomes a different story. If he had the adequate legal gear (18kg/40lb draw, 2.2cm/0.86inch head), the tribe might be able to allow the hunt, I don't know. Different tribes have differing levels of autonomy from the provincial gov't so its within the realm of possibility that its been figured out. A bear is a lot of meat for one guy to process, so I'm not sure it would be a smart idea. A deer maybe, but we arn't seeing footage of a lot of those, and not much evidence of other animals around that would be worth hunting. Don't need a bow to take down a banana slug.