Theories aside, there is no way to lose fat without losing muscle and vice versa, to gain muscle without gaining fat. Increasing protein intake and heavy lifting will help better partitioning, especially in losing more fat. Other interventions, such as protein intake timing, post-workout dextrose, carb and protein cycling, carbless post-cardio etc. may be helpful, but in terms of the effect are closer to the bottom of the list.
There are two pretty distinctive areas in every endeavour: academic and practical. Academic work by itself has produced very few things of value. Most of the time serious advances have been achieved by people in the field. Rocket science was started by crazy guys fiddling with explosives and occasionally getting their fingers blown off in the field. Most medical advances have the same history.
What I am getting at is that it is easy to get lost in details that are not significant for achieving fat loss. BMR calculators are imprecise, so what? Estimate your BMR, plan 20% calorie deficit, eat 2.0 g of protein per day. Re-assess your body composition in two weeks. Adjust accordingly. It is that simple, though not easy, and that's how things have been done by hundreds of bodybuilders for years. Sure, things at the bottom of the list become more important when body fat reaches 10% and less. But for the average person with the body fat of 15 - 20% simply creating deficit, lifting, moving and increasing protein intake will do the trick. That's how pretty much every intervention into a human body works. That's how you treat hypertensives, for example: prescribe a drug, check BP in two weeks, increase the dose or add another drug if not under control. Intervention-feedback-adjustment.
In the case of adding TDDE according to activity - it is a ballpark figure, not precise, but good enough to estimate BMR. As they say in music: close enough for rock'n'roll.
