yes, I didn't state that macronutrients didn't matter (micros have not been shown to matter, lot's of interest in this though so might be the opinion changes at some point).
Maintaining muscle mass whilst losing weight in athletes is different than general population trying to lose weight. (in the former situation protein intake should be around 2 - 2.5g per bodyweight in kilograms a day and some evidence of benefits of fat intake around 1g per bodyweight in kilograms instead of not eating fats at all --> rest coming from carbohydrates). And obviously if trying to maintain muscle mass strength training is given.
Activities do matter some, but not as much as generally believed. There's no "fat burning zone" in low intensity cardio ---> basically beating up your body in multitudes of ways results in increased energy consumption following days (to repair caused damage, slow gradient of EPOC (excessive post exercise oxygen consumption) and for adaptation processes like increased protein synthesis etc.)
This is known and all of this affects the "how much calories you spend" and to lose weight you should eat less than you spend. Which is why I stated Vanster didn't over simplify, but was actually quite precise.
From your example, the two people would lose similar amount of weight in the first month or so. After which the BMR would differ (the other not losing as much of muscle mass or even gaining some, would actually increase his basal metabolic rate as muscle mass uses energy where as fat mass doesn't). so if they didn't adapt in the long run the other would stagnate (he/her would need to keep on decreasing the calories he eats when his mass goes down, where as the others energy consumption would remain high for much longer). The biggest difference being the other would lose alot of muscle mass along with fat mass whilst the other maintained muscle mass much better and only lose fat mass. They both could reach very low levels of fat mass though, other would be overall healthier and perform better in sports (the one with muscle mass), but the other would still get general health benefits of having low fat percentage in comparison to obesity etc.
And yea BMR calculators are approximations, which don't take into account body composition very well. so if you have alot of muscle mass, your BMR is most likely higher than what the calculators give. And if you got none, then the calculators are likely overestimating your consumption.