I have read your reasoning, and even though some people agree with you, I still consider it abuse. You assume that the dog would rather try holistic health practices than die of cancer. Unfortunately, in nature, most animals do not even get cancer... so we have no clue what is a 'natural' treatment for them. In all honesty, most animals I have witnessed who have cancer, have simply stopped eating, made themselves as comfortable as possible, and sat down to die. They don't harbor our human fear of death, and simply do what instinct tells them to do. Nowhere in nature does a dog juice fast. Dogs are carnivores, who eat some plants for the roughage they provide. I think that applying human holistic practices to a captive animal is the equivalent of feeding a diseased human on a diet composed only of bamboo, citing that pandas do not get diabetes.
The animal cannot give its consent-- that is the bottom line. If my cat doesn't feel like eating, I don't blend her food up and force feed her. If she is hungry, I don't withhold her food. Animals generally do what they are supposed to do for themselves. If your dog is still eating, it probably SHOULD still be eating. And if it dies of the cancer, without the dog seeming to try to help itself, I would say that the animal sensed it could not do anything about it and simply wanted to stay comfortable.