Perhaps that really is because basically nobody is assiduous enough about their calorie counting to make it work. But, even if we take that as true for the sake of argument, insofar as the point I'm making is, "This advice has a terrible track record of helping people lose weight," it doesn't work as a counter-argument. Quite the opposite. It works as a supporting argument, by showing one possible reason for why it has such a terrible track record.
I also don't think that it has legs as an idea for how best to reduce the obesity rate. If it were really that easy, then you would expect the population's average BMI to be much higher back when people didn't have the means to effectively calorie count, and it would steadily go down as the means to calorie count more accurately become more widely available. Instead we see that the opposite is true.
Which leaves me thinking that this is an idea whose memetic fitness far exceeds its practical value.
The elephant in the room here is the article itself. The basic premise here is that internal bodily processes can increase your energy expenditure by as much as several thousand calories over the course of the day, even when you're being physically sedentary. And if it can autonomically increase the burn rate, surely it can also autonomically decrease it.
I've certainly noticed that I have a more difficult time thinking clearly on days when I'm not eating as much as usual. I wouldn't be surprised if a similar thing happens if I take a long bike ride without eating any extra food. Though this isn't something I've paid attention to in the past, so I suppose I don't really know. But still, if the body increases calorie expenditure during periods of higher brain activity, then it is certainly just as capable of reducing brain activity in response to a reduction in readily available energy.