It is wise and best to look on all such claims with suspicion. There is always a personal agenda involved in such promotions, and that is selling information or products of one kind or another to facilitate the specific dietary approach. So there is a mixed agenda and a built-in bias as well to over-interpret and to make broad claims, but there is scant evidence because the basic approach here is a misguided one and a false understanding of dietary influences on cancer. There is virtue in avoiding carbohydrate‑based diets that have a high sugar content—that is the culprit in diet, not animal protein or fat.
So a plant-based diet, to the extent it avoids those carbohydrates with a high Glycemic Index, may be an improvement over an omnivorous diet that includes animal protein and fat, but lots of sugar, or carbohydrate-generating sugar through normal metabolism that rises to unhealthy levels as a percentage of the intake. The latter is quite easy to do as almost every prepared food has sugar and this has been done deliberately to worsen things for humanity. It is very difficult to avoid a high sugar intake, in fact, using prepared foods and processed foods available to consumers.
Many of the common foodstuffs people use to avoid eating meat are rapidly converted to sugar following their ingestion and this becomes the major source of calories with very little nutritional value. So while they provide calories, much of it is converted into stored fat anyway and, in the process, ramps up the mitochondrial oxidative metabolism, producing dangerous free radicals of oxygen, and that is the culprit in damaging DNA to cause malignant transformation of cells in producing tumor growth. So the fact that this is one way to reduce sugar is not to say it is a perfect approach using plant-based diets entirely. This is quite unnatural and unhealthy, and is always a compromise, and misses the point about the true dangers.
In reality, it is easy to supply nutrition, a healthy caloric level for energy, a balanced array of nutrients, in a safe fashion with few adulterants, to have a significant proportion of the diet consisting of meat and milk products. They have issues as well from the effects of the consciousness of animals imparted to the food as thought forms, but that can be removed through a simple prayer made before ingestion at mealtimes. It is very, very difficult to have a healthy life on a vegan diet. It can be done but there are many compromises, and it is far from ideal, and there can be long-term liabilities as well.