Saturated fat has little effect on rats, but polyunsaturated fat induces tumors in rats according to to many studies. Low-fat, high calorie diets lead to more tumors than high-fat, low calorie diets in rats (in fact the high-fat, low calorie diets essentially stopped tumor production entirely). This latter was a major study in the journal Cancer Research. Only in high calorie diets was high-fat worse than low-fat, and in low calorie diets, high-fat was better than low-fat.
Atherosclerosis is often observed in pigs, cats, dogs, sheep, cows, horses, reptiles, rats, and baboons when fed exclusively vegetarian diets.
Monkeys in captivity often become fat and diabetic on high-fiber, low-fat, no-cholesterol diets.
It's entirely possible that a no-meat diet is best for humans, but I don't think we're anywhere near the understanding needed to say this -- and his recommendation to avoid fish as well would be viewed as dangerous by much of the medical and scientific community. What we really need are controlled studies, which are entirely possible to do.