With the salt, we're looking at extremely low levels. It's possible the "damage" is already done at a very moderate level of salt intake. The body seems to be able to maintain its sodium levels at a wide range of sodium intake, but once you get down to 30 mg or so, that might be outside of the range that it can adapt to.

Denise Minger show's up in the comments, she makes a good point about dietary fat increasing the insulin response when added to carbohydrate. I think she used the word potentiating. If you think about it--this does make sense of insulin decreasing, at some point, as carbs go up. Suppose you ate just fat and starch. At 30 percent fat, there's lots of fat there. Twenty percent fat might not make much difference. Now cut to three or four percent, like in the rice diet. Carbohydrate intake has gone up 20-40 percent. But that potentiating fat has become nil. What happens to insulin at that point? It's not necessarily higher. Even when you look at accumulation of liver fat--I think it's not that obvious whether this would increase that or not. Fructose increased, check. But postprandial free fatty acids greatly decreased--probably, also check. Something that often happens with diabetics, not always, but often, is that when they begin insulin therapy, liver fat will actually go down. A few things work towards this. Liver increases VLDL triglyceride secretion--bad for blood lipids, but good for the liver. And the triglycerides in the liver come from somewhere, a major source is inappropriately high free fatty acids. Fat trapped in fat cells isn't available to fatten the liver.

All this is moot if the diet is a semi-starvation one that needs whips and incarceration to make it work. But at least some people do experience a decrease in appetite when they switch to a very low fat diet.