While I haven't looked at that particular study, the result you're claiming seems implausible; one would expect humans to be optimized by evolution for living on the ancestral diet. While there are specific reasons why certain parts of our traditional diet are unhealthy (e.g. the ancestral lifestyle burned far more calories than current), in the absence of a specific mechanism like that, "I like me therefore it's good for me" is a perfectly reasonable inference.
And if you're really only interested in health, it seems implausible that that would be 100% correlated with animal vs. non-animal. There are so many different possible food molecules and no reliable common factor that differentiates where they came from - even more so when it comes to the animal byproducts that make vegans different from vegetarians, such as honey.