I haven't done zero carb for enough time to observe this but somehow I don't believe it.

Why would the body just waste all that energy? Sure there might be more thermogenesis and maybe even more lipid excretion in the stool on zero carb, but I don't think it's impossible to gain fat on zero carb.

Were the Inuit skinny as twigs or did they have some added fat to keep them warm in the cold climate?

And don't forget some dietary protein is converted to glucose, and even protein alone will elicit an insulin response.