The above quote, from my dear old mother, is of course not to be taken seriously. Unfortunately, when gullible old people like her take to Google to research matters of health, they are greeted with
countless links promoting natural cures. They don't know how to filter through the muck, they're not knowledgeable about complicated physiological matters, and they're often disillusioned with conventional medicine anyways. Consequently, they easily fall prey to pseudoscience.
In the case of cancer and baking soda, there is absolutely no research suggesting its efficacy as a cure. The main proponent of this treatment is an Italian physician whose license was revoked on account of wrongful death and making misleading claims.
There are trustworthy sources out there who have spoken to the issue, but unfortunately they're far outnumbered by sites proclaiming this to be a miracle cure. Of course, nearly all these miracle cure sites are trying to sell you something. So, the same people that turned away from conventional medicine because they see it as a money-grabbing scheme then fall for a far more transparent scheme under the guise of being a natural cure.
Here are some links that address the subject from factual standpoints:
https://www.caring4cancer.com/go/cancer/nutrition/questions/acid-balance-in-the-body-and-cancer.htm
http://www.quackwatch.org/01QuackeryRelatedTopics/DSH/coral2.html
http://preventcancer.aicr.org/site/News2?page=NewsArticle&id=13441
I should add that this issue hits very close to home for me. My mother is getting pretty old, and she's persuaded by every single field of quackery imaginable. She has total faith in psychics, chiropractors, healing crystals, magnetic bracelets, astrology, reflexology, homeopathy, and just about any other silly thing imaginable. She does at least eat well, but I worry that she'll die prematurely if she continues to refuse to embrace actual forms of treatment.