Don’t know about dementia, but I agree with your theory about low fat/high carb. As Greeneyes says, “I disagree with the food pyramid. What do farmers feed cattle to make them nice and fat? Grains.”
I think you'll find that the digestive systems of cows and humans are somewhat different, especially in their ability to digest cellulose.
I'm not pro grain. The only way I've ever been able to control my weight is on some variant of the Atkins diet. One of the unfortunate side effects of the Atkins diet for me is sleeplessness eventually involving paranoia and general nastiness. I'd rather be a little plump and jolly, weight lift, and walk a bunch than be flat out nuts.
I do think that a person has to watch the grains and keep them in the low to moderate intake. You can’t just omit them all together, but moderation is key. JMHO