That is true, however that fuel does not need to be glucose. As far as I understand it, people eating 3 meals a day and snacks (all containing carbohydrates), their body is not used to relying solely on fat/ketones for energy, and it takes time to adjust.
Also, it's very important when fasting to ensure you're replacing water and electrolytes since once you've burned through your stored glycogen you will have lost quite a bit of water. If you're feeling light headed or out of it, that is one of the causes, whether you're starting a ketogenic diet or fasting.
When I'm fasting I use an electrolyte mix which has sodium, magnesium, phosphorus, potassium and calcium. One of the main reasons for refeeding syndrome is that electrolytes are depleted, and when someone eats again, their cells take up what little electrolytes are left in the blood, which leads to dangerously low levels.