A couple of other issues here. Body fat is not directly usable as energy - it needs to be processed in the liver into ATP, but this is a slow process, and can be a potential chokepoint. On a sustained basis, you are probably looking at around 0.3-0.5 grams of fat oxidation an hour, or 160-270 calories per hour from fat.
The body has reserves of about 2000 calories of usable energy.
Protein and fat are slow to digest (5-7 hours), whereas simple carbs digest in 20 minutes, and complex carbs in a couple of hours.
So with a fat heavy diet, it is still possible to bonk by using up your usable reserves and energy from fat just not becoming available fast enough to replace it, even if you are technically getting enough calories overall. This is the science behind Greg's buddy's problem of not enough carbs during the day.
Personally, I tend to go heavier on fat for meals, and heavier on carbs for snacks through the day. Dinner makes an ideal time for fat consumption, as your body has enough time to process it, and also the body heat generated from slow digestion of fats will help keep you warm throughout the night.
Also, some people here are throwing round some very large calorie numbers. One thing to be aware of is that the standard convention for calorie counting includes your underlying metabolism in exercise figures. This is no big deal for a 30 minute 5K run. But for hiking 12 hours a day, this is substantial double count, and you are probably overestimating calories burned by about 1000.