Yes, it's all so simple isn't it!
I remember back in the 80s I lost a few kilo following a low fat diet (as was the advice then). However, whether the weight loss was due to the low fat diet or not I don't know as I was also eating less generally and going to a gym several times a week.
As with most subjects, the thinking is changing pretty much constantly. People in positions of apparent knowledge (dieticians, gym instructors, etc) can give out the wrong advice too if they are not up to date. And that's if we put aside preference, pet theories and the fact there is conflicting advice (all research based) at any one time.
Clearly, as a simplistic statement 'burn more than you eat' (or 'calories in v calories out') IS correct. Actually it's a statement of the bleeding obvious if you think about it! But it's a blunt tool because it tells you nothing about the HOW. By finding out just a little about the processes involved then you can be a little clever about your weight loss campaign.
With all this diet advice around, it gets confusing! I think different things work for different people. It's a matter of experimenting to find out what works for you. I'm a lazy sod, I like to take the easy way wherever possible and so am not a fan of knocking myself out on a treadmill, but each to their own!