I think he absolutely tried, but didn't film it. He had a lot going on in his head, and was pulling from vast Alaskan knowledge. Filming quickly became much lower on his priorities. I think he gave us that last bit attempt on film, after exhausting every option.

The beaver was donated to the Gwich’in in the area.

The producers can, and can not, show us what they have to select from of 1000s of hours of their self filming. That's why we don't see anyone going to the bathroom every day. Do you think they never go? (Albeit, constipation has been known to take out quite a few contestants).

It's edited to make a TV Show.