The PBS video I linked makes a similar statement. It postulates that the body is always either repairing or regenerating. When you eat it goes into regenerate mode, when you don't it goes into repair mode. The problem is since humans (westerners in particular) can eat all day every day now, the body never enters repair mode. So cancer cells don't get repaired.

Before we lived in cities with huge storages of food we used to hunt. We would gorge on a large kill, then go a long span of time before gorging again. This kept us constantly repairing, making cancer non-existant. At least, thats how the theory goes.

The video explains it a lot better than I.