I used to strongly believe in this until a week ago.
I fit the description given almost perfectly of a male aged 40 who is 6 foot high, weighs 85kg, but losing weight fast on a high fat, high protein and almost no carb diet, taking in just over 3000 calories daily.
Only slightly active.
Done this for the past 5 days and lost 1.5kg, admittedly would be carb depleted, but still dropping weight.
Prior 4 months to this gained about 5kg on a very similar calorie count, maybe 3200 average, but higher carb and lower fat.
Because of this, I no longer believe the simple formula of calories in vs calories out.
Of course I could gain weight on the current diet, but calories would probably have to be maybe 4500 calories daily on this diet.
Plenty of research emerging to support your conclusion too Ace, in particular surrounding sugar consumption.
The only time I lose weight is by going low/no carb and cutting out all processed food, the amount of calories per day has no effect at all.
I don't do apps but love my Garmin Forerunner which lets me program all sorts of interval runs. Its like my own personal trainer.
Interested in hearing more about the Insanity workout - sounds good.