I would argue that yes, sugar is natural, but the degree that people tend to eat sugar these days is unnatural. I'd argue that is the root problem. And to respond to the first image of the comic, that nobody lives past 30, some things I've read suggest that was more due to infant mortality skewing the average, deaths from war, and deaths from what today would be preventable diseases. If an ancient person avoided those three things, they lived quite a long time, and didn't get cancer or heart disease.
I have no exact sources for those last few assertions, it's just what I remember reading (I think also in the Antifragile book).
While sugar (a really generic term usually referring to sucrose) is natural, it occurs in the highly fibrous stalks of sugar cane. Most sugars naturally occur within fiber, while modern food practices extract and/or refine leaving the fiber behind.
The first cartoon tells everything I think about this: http://www.newyorker.com/cartoons/bob-mankoff/cave-cuisine