It is, at least, overly simplified.
The average amount of water in adipose tissue is 13%. In addition to that, it also contains approx. 3% protein. The remainder is fat.
Lard, which should have a similar calorific value as human fat, provides ~8980 calories per kg.
To simplify this calculation we assume that 1 kg of protein provides 4000 calories and 1 kg of fat 9000 calories (in other words ratios of 1:4 and 1:9).
The average kilo of adipose tissue (fat tissue) contains 840g fat and 30g protein. Which amounts to a calorific value of 7680 calories per kilo.
Translated into pounds that is 3484 calories per pound, which is pretty close to the number in question.
The problem is that this is based on average values that have wide ranges attached to them.
The water content of fat tissue can vary between ~4 and ~40% and the protein content between ~2 and ~3.5%.
This means the calorific value can vary between 5540 and 8540 calories per kilo (or 2510 and 3870 per pound) of fat tissue.
Sadly, it also seems that the water content is lower for those above standard weight. So whoever needs to lose a couple of pounds because of health reasons should rather apply 3900 per pound.
The numbers are based on this study. It is a bit old but as the numbers are based on actual tissue samples, I doubt they are too far away from the truth. What might have changed is the average. At least in some countries, as obesity rates are much higher than 50 years ago.
Regarding the water content of body fat, try a watermelon test. Replace an intake of 1000 calories with watermelon worth 500 calories. Drink as much water as you usually do. The extra water intake will most likely lead to an increase body weight on the next day, even though your calorific intake was lower.
The above-mentioned study refers to: "THE CHEMICAL COMPOSITION OF ADIPOSE TISSUE OF MAN AND MICE." LORETTE W. THOMAS, Department of Physiology, Edinburgh University. (1962)