Cancer and other degenerate diseases weren't an issue at a time when people lived, on average, 35 years. Cancer mostly affects people over the age of 50. While you can get cancer at a younger age, it's less common. Not impossible, but unlikely. So the population was far more likely to die of other causes and other diseases than Cancer and even if they DID die of cancer, how would they know? It wasn't common practice to do an autopsy on someone after they die. In fact, the only way they knew (or thought they knew) that someone died was to do a Wake. The tradition of a wake prior to funerals was created to ensure that the person really was dead. They would lie them on a table in the middle of the home for 3 days. If they didn't wake up, they were declared dead and buried. Some of them woke up in their graves as indicated by scratch marks on the inside of the coffins during the body moving of the time. Yes, to save free up graveyard space they moved bodies out of individual graves and into mass graves.
I also took a look at the books you linked on Amazon. They're by the same author. I went to this person's website and right there on the front page is a disclaimer saying that the information on the site is for "educational purposes only" and that you should consult your physician. Sounds to me like she doesn't believe in it either. But I suspect you'll claim it's because of the evil science that would try to discredit and destroy her legally if she didn't protect herself yet I ask, why would she need protection if it worked?
Anyway, tribal medicine is not, by itself, incompatible with modern medicine. However, modern medicine is a refined form. Me and my friend were having this discussion last week.
In Ancient Egypt, it was a practice to apply honey to a wound. Modern medicine, however, doesn't apply honey but rather the chemical IN honey that helps. Modern medicine takes an herb and finds out what in that herb gives the effect and uses that in a pure form rather than a mix of other herbs that may not help at all.
Modern medicine also uses bacteria, germs, and viruses to help explain illnesses which makes a lot more sense. The 4 Humors don't exactly tell you how a family can get sick at roughly the same time during winter. After all, how do they transfer phlegm to one another to produce an imbalance in everyone?