And the fact is, there are not numerous studies consistently showing a correlation, there are many studies that do not show that those who eat more meat get more disease. For example, Cretan villagers have lower heart-disease rates than even the Japanese and eat diets consisting of 40% fat. The "French Paradox" is so termed because the French eat high quantities of animal fat but have low heart disease. Tokelauan's, who had a diet high in fat (50% fat) and saturated fat (90% of the fat they ate was saturated), were relatively healthy. After migrating they consumed much less fat and had higher heart disease.
In other words, there's a lot about diet we don't understand yet and you can't boost the relevance of epidemiological studies by saying that "virtually nothing is proven ever" and therefore we should just accept observational science, when it's known that epidemiology has significant flaws as anything other than a hypothesis generator.