I don't think it's half-plausible to compare Hadza or Intuit diets to a Big Mac and a soda. Neither transfats nor processed sugars are in the Hadza diet, just for example.
Isn't honey a processed sugar? The processing being done by a bee instead of a machine
By this "reasoning", all food is processed amino acids and related elements. But despite such sophistry, there's a measurable difference between a human-machine-processed diet and an animal-processed diet. Good figure.
What is the measurable difference after controlling for what the OP listed?
We could absolutely decimate the Intuit by introducing free Pepsi coolers in every home.