Perhaps the reason women do not get improved insulin sensitivity on a high protein diet is. 
When the body has assimilated all of the amino acids from dietary sources for anabolic needs. It converts the bulk of the excess into glucose through gluconeogenesis. This will result in insulin release and further insulin resistance.
The authors did not mention the increasingly popular "ketogenic diet"  When a diet has minimal carbs and only metabolically required amino acids. The calories used for energy requirements come from fatty acids and insulin resistance melts away. 
This low insulin state results in suppressing MTOR and promoting autophagy, Perhaps the writers could elaborate further.