This is innacurate if not simply false; according to the WHO red meat is a class 2 carcinogenic and sausages are class 1 carcinogenic. This leaves only white meat as non cancerogenic
If you look at the data vegan (and vegetarian to a lesser extent) diets over various studies consitently perform better in cardiovascular health and cancer rate (colon in particular) compared to the omnivorous conterpart