I saw that phrase and thought it was pretty weird. Hunting wild animals for food is not some fringe thing that happens in "other places" I've eaten tons of fish, duck, deer, elk, etc. that were all "wild animals".
Absolutely agree, but poison doesn't exactly spread like an infection. Plus I guess most herbivorous animals by now do have a fair bit of intuition what to eat and what not to.
Simply put, you catch fewer(near 0) infections eating plants. Even more so for animals in the wild.