There are many stories and anecdotes (from doctors as well as non-doctors) about advanced cancer just disappearing for no explainable reason. There is much we don’t know about why cancer goes into remission (in the absence of anti-cancer drugs and therapies.) It is possible that diet can cause cancer remission in some cases.
In fact, I did a quick search on Google Scholar and found this: a study called “Case Report: Spontaneous Remission of Metastatic Endometrial Carcinoma Through the Lim Lifestyle,” in the scientific journal Nutrition and Cancer, discussing two cases in which cancer had gone into remission apparently as a result of the Lim Lifestyle, which involves a vegan diet. (There is even a book called History of Alternative Cancer Diets.)
That said, although I am familiar with a vegan diet being prescribed by some doctors to treat heart disease, I have never heard it touted as a surefire treatment for cancer, and I would be very surprised if it works in all (or even most) cases.
There are people who think homeopathy can cure cancer but there’s some vast conspiracy covering up this knowledge to benefit cancer drug companies or something. Be careful — people have died because they refused regular treatments in favor of ineffective alternative treatments. That’s not to say alternative medicine doesn’t ever work — I’m just advocating skepticism of any claims that such a therapy always works or is unpopular only because of mysterious dark forces controlling the world.