Vegetarians and groups promoting vegetarianism often promote it as a healthier diet, particularly one that results in lower incidences of diseases such as cancer and diabetes.
While there is often statistical survey data to back up those claims, that kind of data is never really enough. One can never be sure that the survey has captured all possible components of a person's lifestyle, nor that they have been truthful. Lastly, it's not always clear what is cause and what is effect.
Researchers at UCSD have, however, found the missing medical link that demonstrates how high-fat diets can lead directly to diabetes. Source: MedGadget.
I hasten to caution: you can find a way to eat a high-fat vegetarian diet. Unfortunately I often find that way...eating too much cheese, mostly. But I'd say the majority of vegetarians, and certainly vegans, are much healthier than I.
It's all a little complicated for me to go into greater detail about, but I thought it was worth pointing out.