Quite funny, had to reflect on my own bias a bit. I still think it's important to be critical of purely observational or anecdotal results when tested evidence driven medicine does exist. For example, suggesting a cancer patient abstain from radiation therapy, offering the alternative of cayenne pepper smoothies.
The study has all the statistical bells and whistles. And its result perfectly matches our understanding of cancer spread process - local overproduction of acid from glucose aerobic glycolysis (dominating way of glucose consumption by cancer cells) results in dissolution of the ECM (which is mostly collagen) - and the probable mechanism of action of the baking soda on it.