Yes, MICHELLEXXXX is absolutely right--it is not a "fact" that our brains need carbohydrates. The fact that is being twisted around here is that our brains need GLUCOSE.
Our bodies can convert fat into glucose. When we limit our intake of dietary carbs, our liver is able to convert amino acids to glucose. The fat we eat provides energy (fuel) for this process to happen. Whatever fat is unused in that process is converted to ketones, which in turn reduce the need for glucose. This process of synthesising glucose from protein is called gluconeogenesis. Glucose can also come from glycerol, which is a by-product of fat metabolism, and can come from both dietary fat and adipose tissue. See the link at the end of my post for this study.
If our brains needed 130g dietary carbohydrate to work, I would surely be dead or knocking on death's door by now, as I've kept my carbs well under that amount for some time now. Same goes for a number of other SP who also eat low carb diets and are thriving. In fact, I find that my brain functions better on a carb-limited diet than it did when I ate all sorts of carbs.
Another point I've got to clarify, yet again-- the notion that low carb diets "eliminate fruits and vegetables" is another bit of disinformation that is frequently spread by those opposed to this way of eating. This is simply not true! I eat a rather large portion of vegetables at every meal, including breakfast. I also eat fruit, though not as freely as vegetables due to the sugar content. I can only assume this untruth is based on the very temporary induction period of the Atkins Diet (Atkins being only one version of many low carb diets).
Glycerol gluconeogenesis in fasting humans: www.ncbi.nlm.nih.gov/pubmed/7647479