One possibility is sensitivity to gluten or other foods. When people go keto, they are inherently not eating anywhere near as much gluten (if any) than if they were eating carbohydrates. If they've only tested "keto" but never tested "gluten free", and are indeed sensitive to gluten (like I am), they would put the solution down as "keto" when in fact it was going gluten-free. Same phenomena to be applied with fasting.
Not saying this applies to all or even majority of cases that claim fasting/keto/etc is their cure. Just throwing this out there as something people should be aware of when testing these things.