As a scientist, I find that "correlation is not causation" is both simple and yet very counter-intuitive for many. Same with "anecdote is not evidence." In college, a professor will often use the famous example of butter consumption and divorce rates in Maine. Worth googling, maybe.
People have immune systems. They often get better due to the working of that system. If you give someone a Tic-Tac and tell them it's a drug that will make them better, this will improve the patient's mood and expectations of a positive outcome. This state of mind has been observed to stimulate various physical changes in the body, including boosting the immune system. In some studies, it's been shown you don't even have to say anything about the sugar pill. The placebo effect still works. It's why witch doctors were actually effective - the patient believed in their powers, and their immune system mobilized. Now, here's the key fact for you: there is one thing that's stronger in its effect than a placebo, and that thing is a medicine with actual curative action. Two acetaminophen tabs, for example, knock down a headache better than two sugar pills.
Chemo shrinks tumors better than apricot pits.
How do we know this? Double-blind clinical trials with randomized administration of the med, in which neither patient nor doser know if it's real or placebo. If the group getting the real med does better than the sugar pill group, it is indicative of a genuine physical effect beyond the psychological one. Then further study will try to find what exactly that mechanism is, so it can be further enhanced. With chemo, it happens to be the drug stops protein synthesis and the tumor can no longer grow or maintain the existing cancerous cells. That's why your hair falls out - your follicles are also failing in protein synthesis.