Yes, I do believe the body is running on its own fat stores at night.
In a person with normal metabolism who eats the way you and I do, this would be constant during both day and night. This process is highly dependent on cortisol. For ketosis and zero carb to work your cortisol must be normal. If it's low the body can't burn fat for energy as well, coupled with a higher insulin level because cortisol helps tell the body when to shut off insulin production. Mix in a lowered blood Sugar level because of this and you get the weird situation of ketosis, but hypoglycemic too which should never happen in a healthy person.
Another piece of evidence suggesting that cortisol is at the heart of our issues.