That is oversimplified and it does not change my argument at all.
Satiety is both physical and hormonal, so volume and fat can make you full but insulin can override that.
I can eat way more volume of carrots than brisket because fat is satiating. A small portion of fatty meat makes me feel full even though my stomach volume is not nearly capacity.
A study has shown that oral stimulation with different fats by modified-sham-feeding (MSF) resulted in increased feelings of satiety compared with water in human subjects, with linoleic acid showing the strongest response (Smeets and Westerterp-Plantenga, 2006). On the other hand, sham feeding a high-fat cake increased food intake at the next meal compared to nonfat cake in restrained eaters (Crystal and Teff, 2006).
Without any volume ingested, fat increases satiety but fat+sugar reduces it.