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There haven't been enough studies which control for other non diet lifestyle factors.
People on vegan diets have measurably lower rates of heart disease, type 2 diabetes and cerebrovascular disease.
Does that study take into account the "healthy" aspect of the question? Were the vegan diets compared to "healthy" omnivore diets or was it a random sample of vegans, who by definition are more concerned about their diet, and a bunch of regular people eating fast food?
The source states that "the [mortality rate] for vegans was very uncertain (anywhere between 0.7 and 1.44) due to too few data points."
It can back up that eating less meat, or no meat is healthier than average, it can't back up that veganism is healthier.