3500 is an average/approximation that attempts to take into account all the considerations mentioned in the comments and more:
- human fat is mixed with other types of tissue,
- fat grams actually fall in a range of calories,
- not everything eaten is absorbed,
- the fat content of foods is not consistent,
If I could eat somewhere between 3000 and 4000 calories without burning any, I could expect to gain about a pound of stored fat. If I could burn somewhere between 3000 and 4000 calories without eating anything in the meantime, I could expect to lose around a pound of stored fat. However, those statements are approximate and impossible to implement.
This USDA document (dated 1973)
describes how the calorie contents and nutrient components of specific foods were determined. Using a "bomb calorimeter", a sample of the food is burned and the heat produced is used to heat a known quantity of water. The temperature of the water is measured before and after and the number of [kilo-]calories of energy produced by the food sample can be computed from that difference.
Those numbers are published in USDA "Standard Reference" documents that manufacturers and researchers (in the US, anyway) use to compute calorie numbers for actual foods based on weight and nutrient content (how many fat grams, protein grams, carb grams are in the food). That's the information that winds up on packaged food nutrition labels.
However, the nutrient and calorie content of food can vary. Here's an FDA document that discusses that issue. So you can't eat the food sample that was measured and we can't measure the food sample that you ate, and there's no guarantee they contain the same number of calories per unit of weight.
Most foods that we eat are not pure fat. Oils and lard come closest, but who eats oil or lard alone? We normally eat a mixture of fat, protein, and carbohydrate. A healthy diet includes a fair amount of fiber. The more fiber consumed, the more calories pass through and are excreted rather than absorbed.
For the average person, trying to remember to record every single calorie consumed is overwhelming. The mint I snagged off my co-worker's desk? The cookies somebody brought to a meeting that I wasn't expecting that I ate three of? (and how could I possibly know how many calories are in a homemade cookie?) The extra soda yesterday afternoon because I was falling asleep?
So in practical terms, on a day to day basis, it's extremely difficult to account for all the variables and accurately track one's caloric intake.
Similarly, it's next to impossible to accurately track one's caloric expenditure. As we exercise and become more fit, the body becomes more efficient. An exercise that burned 400 calories a few months ago may only burn 300 or 250 today.
Another piece of conventional wisdom (called out in the HuffPost article linked in the question) is that a gram of fat contains 9 calories. Again, the 9 cal/gram number is an average. Zoe Harcombe points out in her article linked in the question that she found references for a range from 8.7 to 9.5 for this value. There are 454.5 grams in a pound (based on 2.2 pounds in 1 Kg = 1000 grams). 9 * 454.5 =~ 4090. So according to that, there are approximately a little over 4000 calories in a pound of fat.
Another place we can look for a reference is online food calorie databases like calorieking.com or nutritiondata.com. I went to nutritiondata.com and looked up "olive oil". One of the hits is "Oil, olive, salad or cooking", which is listed as having 884 calories per 100 grams. (884/100) * 454.5 =~ 4018 calories. Other types of fat (canola oil, peanut oil, lard) give similar numbers. Scrolling to the bottom of the page, I see "Source: Nutrient data for this listing was provided by USDA SR-21."
Googling "USDA SR-21", I find this page: http://www.ars.usda.gov/News/docs.htm?docid=18880 which says that "SR" stands for "Standard Reference" and the current version is SR-27, so one of the most respected online sources for nutrition information (nutritiondata.com) is six versions behind the most recent data. This is the "Standard Reference" document I mentioned earlier.
So the original numbers are estimates based on averages from bomb calorimeter measurements made some time in the past. Those estimates are then extrapolated and crunched and rejiggered and reported to more significant digits than is justifiable.
Often calorie numbers are bandied about and used in computations as if they are accurate to 1% or so. Actually, I believe the error is typically on the order of 30% to 50%.