I have my own personal research data.
I monitored my fat loss using the tape measure methods combined with weight in kg over 3 years, half the time I would be strict at different monthly intervals. Male, 27 through to 31 years at 175 cm tall weight range between 68 and 77. I put muscle on easy but also gain weight easy but that's because I love food way too much.
Anyway I was losing 2cm a week from my stomach circumference with average daily deficit of approximately 4000kj, this equates to 1kg of body fat in my calculations per week, note that's body fat not total weight.
After calculating this you can see I burn 28000 kj in order to have lost 1kg of body fat.
I guess the science was almost right for me, but my body seems to put out extreme amounts of heat compared to most people, I notice out most when sleeping. My body is hot with no covers while my girlfriend is cold and covered up. Knowing this kj level really helps for me when I need to lose weight because it's an easy goal to aim for.
I should note this weight loss was not increased with cardio, I tried half of the time with no exercise more than sitting and walking to buy groceries, however every day I try to build/maintain my muscles with stretch bands for less than 15 minutes a day. the other half of the time when I had the same level of daily kj deficit I was performing long periods of intense cardio.
the research out there seems correct, your daily deficit is the most important factor in weight loss.
I should also note I didn't pay attention to how many carbs I ate however I did try to limit my fat intake, when it came to carbs I couldn't care less, I love pasta and rice too much. I think low carb diets are not effective, but eat protein when you can.