Hello, I'm a Chemist.
Even Pauling's quote about all disease being traced to a mineral deficiency, though extreme, can at least loosely be tied to many diseases.
For example, lets say you have a genetic predisposition toward a particular form of Cancer. And lets say you increase your risk by unhealthy lifestyle. The body has levels of defense against this disease progressing (utilizing enzymes that rely on minerals), and while I am hesitant to go to the extreme of saying all disease is tied to mineral deficiency alone, your risk is certainly compounded by the lack of proper nutrients.
While there are thresholds past which even full, adequate nutrition and supplements alone will not save you (breathe enough carbon monoxide, inhale enough coal dust, allergic reactions, etc.), a primary role of proper nutrition is not weight loss (which is where most people focus) but in running the body smoothly, efficiently... And that includes the physiological process of disease prevention and repair.