This is true. In the pre-civilization past, substantial obesity was almost impossible. This is due to several aspects of modernity, and not just food availability:

- compared to us, ancient humans had to spend a LOT of energy just to survive. You want clothing? tools? food? Shelter? You're making it. You're finding it. You're preparing it. Every day. Or else you don't make it.

- Parasite & pathogen load. A substantial amount of body resources used to go to parasites like helminths, as well as to fighting off infections. In modern, post-industrial societies almost all parasites are simply eradicated. When you do get infections, you get medical care (antibiotics, vaccinations, antivirals, etc) that drastically reduce the strain on the immune system and energetic resources required.

- Obesity, at a certain point, is debilitating. But modern society makes such a life quite manageable. This was far less true in the distant past. No rascal scooters on the savanna. Many groups of humans were nomadic. If you can't walk and run reasonable well for hours at a time, you're in a lot of trouble.