One thing that isn't often mentioned, your brain needs protein. It doesn't run on carbs or fat. So while your body will be fine, your brain is going to be eating your body to keep going, and the one tool you need to be working is the mush in your skull.
you need water to to DIGEST protein, but most of the starvation research is either incomplete or flawed, so its hard to say all of whats actually going on as far as the later stages. We know the basics, and you start using your own bodies fat first, and its used when ketosis starts (leading to so called "rabbit starvation") But a lot of whats going on is based on what you eat normally, and epigenetics. For the 72 hour situation, you just want calories. any and all, and a mix is best, but take what you can get. nutrient content doesn't usually matter for a while, its pretty hard to actually get a deficiency if you start out healthy.
As for that comment about needing carbs to burn fat, I don't see how that can be true, as in starvation the body burns off the fat pretty quick.
From my personal experience:
Sugar- quick spike, and crash, can start a feedback loop of bigger highs, and harder crashes over a surprisingly short period of time.
Complex carbs - same as sugar just longer rise and fall, but if all you have is carbs, things get just as bad, just slightly slower
Protein- long burn - not necessarily "energy" but keeps hunger off longer, and keeps muscles and brain working longer.
Fat- longest burn, best for keeping warm. Fat calories seem better at keeping sustained heat in cooler conditions.
If I had to pick just one for a 72 hour stretch, I would pick protein provided water was sufficient.