Remember we are talking averages here. Those who choose a vegetarian or vegan diet are a self selected group of people for whom health and taking care of themselves, as well as having strong ethical beliefs is important.
This cannot be said of the wider meat eating population, many of whom, will have a poor diet, and include overweight people and those that drink and smoke. All factors, more likely to be found in omnivores than vegans.
To find out if vegans were more healthy, you would have to match them against a sample of meat eaters who
will have a matching age range (more young people are vegan than older people) equally proportions of those that are overweight, heavy drinkers and smokers, levels of fitness, presence of other medical conditions etc etc.
I haven't seen this survey, so know nothing about the sample and who did it, but I would need much much more information before I would believe it.