IMHO, it's the liver dump from converting protein to glucose (gluconeogenesis) or releasing stored glucose in form of glycogen rather than burning fat in the early morning hours. The higher Bgs are due to either low insulin (insulin deficiency) or inability to utilize normal or even high insulin levels. Liver does it's job pretty well of keeping us from too low BGs while we asleep and in general, during the day as well. Low or inefficinet insulin equal higher glucogen. Diabetics have problems with FBG for above reasons. As for getting higher Bgs from burning body fat, it's actually the other way around, high BGs mean the body cells are starvng and muscle protein is burned to satisfy some of the immediate needs. Some fat will be burned as well, but a great deal of muslces is usually burned first.It's much easier for the body to burn muscle than fat. Fat is body emmergency supply.
I'm not sure that normally our body burnes dietary protein for energy, it's either carbs or fat. Protein is used for repair muslces and other body tissues. I guess when body burns fat it's mostly due to a negative calorie balance or ketosis. Getting higher BGs while burning fat is more ketoacidosis and should be avoided at all cost.
I can add some more mud, may be this will make it clear. The best answer is in Ketogenic diet book by L.McDonald. You can also find some of his articles here
http://www.naturalphysiques.com/cms...ount=0&blogid=1
D.