Thanks for posting that piece from Stefansson's book. I haven't read the original, just bits from others referencing it.
Here's a passage from The Art and Science of Low Carbohydrate Living 2011 Stephen D. Phinney, Jeff S. Volek
Among the Inuit, when a seal or caribou was killed, the fat was saved for human consumption (or lamp fuel) and the leaner parts were given to the dogs (or any gullible ‘white guys’ in the party). Farther to the south, when a spring buffalo (i.e., one that had yet to rebuild body fat reserves after the winter) was killed on the Great Plains, the humans ate the tongue, liver, and marrow. These tissues tended to retain their fat content even during periods of privation. The lean meat was either dried (to serve as an emergency food source) or fed to the dogs. This differential partitioning of the kill actually makes a lot of sense, as a dog’s metabolism is much more tolerant of a high protein intake than is that of a human.
And here's a blurb about Vilhjalmur Stefansson eating organ meats while proving one could survive on an Inuit inspired no carb diet, from http://discovermagazine.com/2004/oct/inuit-paradox/ (I've read similar elsewhere but this was the first referenceable source I stumbled upon)
"In 1928, to convince skeptics, he and a young colleague spent a year on an Americanized version of the diet under medical supervision at Bellevue Hospital in New York City. The pair ate steaks, chops, organ meats like brain and liver, poultry, fish, and fat with gusto."
I've read in other places of the Inuit making bone broth and eating whale skin. If you think it important I can attempt to find other references.
I should not have said they ate the whole animal, but rather they ate multiple parts from multiple species coming from a natural intact ecosystem as in contrast to only eating steak. For 30 days, deficiency is not a major risk as people can fast for that period of time without suffering diseases of deficiency. Protein poisoning, aka "rabbit starvation" is perhaps a risk but Brenda shifted to higher fat cuts of meat avoiding that problem.