Well I think under-eating tanks the thyroid and I believe she was still under-eating when she was doing Paleo. She mentioned that she only started feeling better when re-introducing carbs and making sure she's getting enough calories, so does low-carb tank the thyroid too, or only when you under-eat on it as with on any other diet would do is what I question, or both?
I do agree that they are all probably eating too much fat and believe that you can't ease the carbs in and slowly reduce you fat without the excess fat causing reactions with the carbs. I think most people have to kinda do it cold turkey and stop eating excess fat as they bring in all the carbs.