Often, there is still a genetic predisposition to cancer, heart disease, and other illnesses. Having BRCA (1,2) genes, for example, puts women at a much greater risk for being diagnosed with breast cancer...at birth, before anything has even had time to intervene. So even if she eats everything right, I don't think it would be fair to blame her for failing to control her body. Cancer research money led to the discovery of those factors so that women could be tested (if they wanted to) to understand their increased risk so that they could manage lifestyle factors, or in extreme cases, consider removing their breasts.
Environmental causes, such as radiation from natural disaster/war, etc. also play a role. At a high enough dose of say radiation, I think it would be difficult to try and control the affected through diet alone. I don't think diet alone will end cancer diagnoses.
I don't think those organizations are directly tied to pharmaceutical companies. True, they do tend to advocate for low-fat diets and adhere to other CW guidelines, but they also raise awareness, give advice about pre-cancer screenings, exercise, quitting smoking and offer hope to those who are already suffering. Prevention is great (if you are interested in ancestral approaches), but I have doubts that diet alone will save someone who is in stage 3 and hoping for a cure.
Organizations like that aren't only interested in the cure. They also invest in understanding the interplay between biological causes, emotional reactions (I worked on a breast cancer research project investigating family members of those diagnosed) in the affected and their family members, and environmental causes (e.g. BPA). They do tests on cortisol and recovery rates, how social support affects recovery, etc. It is much more than just the body.
I guess I'm not sure what you mean by "conventional" non-profits. Organizations like that also give survivors a chance to celebrate life through walks and meeting others.
I may be biased because I used to run with a children's brain tumor foundation. The organization also raised money to have an author write a book for young children confused about their medical condition, sent children with illnesses to special summer camps for those who couldn't afford it, and in general, gave parents a chance to meet eachother through walks and socialize and connect. There's a community element to many non-profits. It's not just about the "biology" behind things.