From what I've read about protein poisoning/rabbit starvation, the issue is a complete lack of fats in the diet. The malnutrition symptoms are pretty bad, and it's telling that cravings can only be satisfied by eating fats and oils.
What confuses me is the few times they attempt to quantify how much fat we need. Nothing precise, but I've read as much as 50/50 meat and fat from an animal. I don't eat nearly that much fat, I think, and yet I'm clearly not suffering from protein poisoning (to be more precise, a typical meal has a small handful of starchy carbs, a similar volume in meat or fish, and almost twice that volume in cooked greens).
Is there just a lot of invisible fat in our food, or does some other vital nutrient come into play?