Folks might be confusing description and prescription here.
SAD = refined fat + refined carb
Primal = unrefined fat + unrefined carb
All fat is by nature hydrophobic (H2O fraction = 0%) so exchanging bad fat for good fat--while tremendously important and beneficial--won't affect the energy content of your food.
By contrast, a defining feature of refined carbs is dehydration which multiplies the energy density tremendously. Cereal/bread/chips have ~3x more carbs per bite than a banana or potato and ~5x more than other stuff like beets and squashes. Our eating behavior doesn't run on a simple calorimeter so we inevitably take in more.
So anyone who switches to unrefined food is probably going to drop a lot of carbs even if they neglect to track them.
Lots of: urban hiking, cycling, sprinting
Lots of: fresh meat, seafood, eggs, organs, tubers, starchy fruits, low-energy plants, meat fat, dairy fat, oily fruits
Some: cured meat, dairy protein, sweet fruits, rice, peas, tree nuts, oily seeds
Minimal: soy, refined proteins, sugar, liquid carbohydrate, grains, beans, refined oils, peanuts