I'm usually all about investigations like this but the repeated claims that obesity is, for sure, not caused by diet is a leap. Also, the claim "people ate worse in the past (bread and lard)" doesn't ring true and is unsubstantiated.
My own opinion: we are seeing what happens when we combine an increasingly sedentary lifestyle with eating mass produced, low quality foods. Fruits and vegetables are becoming decreasingly nutritious. Animals (even organic) are force fed poor diets to slaughter them a few days earlier, whose fats contain high concentrations of these poor diets. There are lots of examples of food quality going down.
I especially think the problem is related to a combination of excessive carb intake, and PUFAs (think vegetable / seed oils found in a huge portion and variety of foods). There is a growing body of research this is the case [1].
DYOR.