I am not quite clear on the hand waving thing. Also, some of what I wrote is because I know if I did not write it, someone would say that they could not lose fat on that kind of diet, kind of like one of my ex-gf, lol.
Anyways, as simply and as brief as I can...You tell your body what to burn based on what you feed it. At all times our bodies are burning fuel on a spectrum. So, someone may be burning 70% carbs/20% protein (includes muscle)/10% fat. Well, insulin tells the body that it is ok to burn carbs and protein. This is because your body perceives that carbs are in abundance. Insulin also signals the body to store as much as it can into fat. Ketosis tells it to preferentially burn fat. It is like tricking the body into thinking that food is scarce, so it should burn it's fat stores. But there are other important factors, like if your muscles are fully compensated with glycogen, then your body will not burn fat as much as if they were depleted. This is the main reason for the 2 workouts right after the carb up on a ckd.
Ok, there it was simple and short. There are tons of holes there, and if you want the full skinny, pick up a copy of Lyle McDonalds book The Ketogenic Dieting Guide (or something like that, it has a maroon cover). Also, you could join the low carbers list, although it is nowhere near as good as it was 2-3 years ago.
hth
txlonghorn