Look at supermarkets: everything after the department for fruits an vegetables is basically bad for us. Science prooves that. But we have to pass all this convenience food that promises to be cheap and fast and healthy and it isn't. And most people somehow learned that in school but ever since they are being informed by the companies.
I will agree with your objection to the “prove” claim about the science (if only because it’s an overstatement of what science does) but the negative associations between various adverse health outcomes and a plant-based diet are well-supported in the literature: lower risk of type 2 diabetes, lower systolic BP, lower risk of cardiovascular events, lower total cardiovascular mortality, lower rates of certain malignancies.