My first question on reading that was "Where did she get that figure, 130 grams?" Doing a few searches, the reference I find is a recommendation released by the Institute of Medicine, part of the National Academy of Sciences.
Here is a summary (PDF). It does not say "that's the minimum your brain needs to survive." It says, "RDA based on its <carbohydrate's> role as primary energy source for the brain." She's misstating the case.
I haven't found anything saying what science they based this on, and they don't state anything dire about having less than 130 in the document.
As far as the kidney failure, etc. she is conflating the problem of
ketoacidosis with simple
ketosis. Some people (like those with liver or kidney disease) cannot eat very low carb, at risk of ketoacidosis. Most people do not have this problem.
She said you would increase your risk of
cancer by eating low-carb? I think she's out of her
mind for saying that. If you don't get enough fiber, you can increase your risk of colon cancer, but I think most low-carbers actually do consider fiber intake very carefully.
She's wrong about the 1-pound figure. It's higher, it's something like 2.5 or 3 pounds, but that's not terribly realistic for most people. She is right in that slow weight loss is best; however, when low-carbing you lose some serious water weight at first, and that's nothing to be afraid of.