So a few things.

1) The abstract of the study states "...the aim of our study was to analyze differences between different dietary habit groups in terms of health-related variables." That's a very different thing than saying "the aim of our study was to analyze differences between different DIETS in terms of health-related variables." So we're talking about vegetarians... not a vegetarian diet. And we're talking about girls only, for all intents and purposes - 40% under 30, 76% female. If you wanted to take a swing at a meat-free diet, this isn't how you'd do it. If you wanted to conclude that young vegetarian women are less healthy than they think they are, bam. FTA:

Therefore, public health programs are needed in order to reduce the health risk due to nutritional factors.

2) Moby put a little factoid in the liner notes of one of his albums arguing that one cow consumes as many resources as like five acres of wheat or something like that. Yeah, Moby, but I only have to eat one cow. That's the point. Predators exist because herbavores are excellent concentrators of nutrients and energy. That's why ungulates stand out in the middle of a field chewing all goddamn day but lions only mosey out from under the trees every couple days to work up a sweat and tear up some flesh. Adventurers have relied on hardtack and pemmican for millennia, not fruits and berries. If you had to map the Louisiana Purchase without depending on meat you'd be fucked.

3) There are advantages to a vegetarian lifestyle from a health perspective but you really have to work at it. My wife has vegetarian patients regularly - women who are building babies without eating meat. And unlike non-pregnant vegetarians, these women get regular blood tests and health examinations... which means my wife can quote their own lab results when she says "you're gonna need a lot more protein." It's a slog matching a vegetarian diet to a carnivorous diet nutrient-for-nutrient. Calorie-for-calorie? No sweat. Carbs are everywhere. Protein's a bitch, though. Nuts are no match for fish. Fish is no match for chicken. Chicken is no match for pork. And beef? beef's got some protein. My vegetarian friends tend to be pragmatic vegetarians - when they're overseas, they eat meat because being a vegetarian in Vietnam or Thailand is a laughable pursuit. You just can't find the protein.

We've got pointy teeth. We've got a digestive system evolved to process high concentrations of fat and protein. That doesn't mean we have to eat meat, but if we don't, we're at a disadvantage. That disadvantage typically manifests itself as increased cost, increased effort and increased vigilance. Should you lack any of these three you end up with a substandard nutritional balance and a substandard nutritional balance leads to health concerns. This study doesn't say "a vegetarian diet is unhealthy" it says "the people surveyed had poorer health outcomes the less meat they ate."

We're also talking exclusively about Austrians. I don't know that much about the Austrian diet, but if it's anything like the Swiss diet, avoiding meat is a stone-cold bitch. Might as well be in Vietnam.

Your friends might very well be those uber-healthy vegetarians that have a perfectly balanced diet. If so, good on 'em. Let 'em be offended. They might not be, though. It's been my experience (and, vicariously, my wife's experience, 'cuz she's worked with a lot of vegetarian women and looked at a lot of data) that vegetarians tend to be less healthy than they think they are because they underestimate the amount of energy they're getting from carbs and overestimate the amount of nutrients their diet provides.

And that's pretty much what the study says - "you're not as healthy as you think" not "the core philosophy of your diet is flawed."