I can't really comment on the facts since I neither read all the studies or had time to watch the whole video.
I'm not an expert in nutrition so this is my personal opinion. I think he's raising some valid points:
* It's a surprisingly difficult subject to study.
* There're a lot of bad studies.
* There're a lot of dubious conclusions.
However, losing weight is just a matter of energy balance. If you consume less energy then you "use", you will lose weight. Consuming less can be done in many different ways. As can "using" more. Different diets may however bring additional advantages (such as decreased risk of cancer).
It also depends on what you are doing with your body, for example, you won't find many tour de France cyclist eating low carb before a race.