I don't think it's something that can be dismissed as "false" so easily. The best argument I've heard as far as why some people can be healthy eating meat-free diets and others cannot, is the example of moving an animal that is native to one continent to another continent across the world and expecting it to survive. Even if you could somehow account for the climate change, an animal from Australia for example most likely could not live in the wild in North America because it probably wouldn't be accustomed to eating North American food sources nor would it likely be equipped to digest them properly. The animal would grow weaker, get sick, and eventually die.
It's similar for people...different cultures have grown accustomed to eating different types of food based on the regional availability of those foods, cultural differences, and so on. There are many cultures (Asian cultures specifically, iirc) that have a high incidence of adults who are lactose intolerant, for example - that's not just a coincidence. In the same vein, some people simply are not able to efficiently absorb certain nutrients, such as iron, from plant sources. If your ancestors relied heavily on meat to get their nutrients, you probably don't have quite the same enzymes as your friend whose ancestors relied more on plant sources for food. Eating a vegetarian diet can be healthier, but I think that studies showing this can be skewed...first off, I'm not sure they can even fully account for heritage like I mentioned above. Also, the typical American meat & potatoes diet isn't unhealthy solely because we eat meat, but because we eat *a lot* more meat than we need to, and because we eat a lot of processed foods, saturated fat, don't exercise enough, etc. (I guess I should put in the disclaimer here that I haven't really read many studies on vegetarian vs. omnivore diets, it's just my opinion.)
I do think it would be in our best interest to put a stop to - or at least cut back on - factory farming of animals, because the system how it is now is a huge source of pollution (not to mention the animal cruelty), but giving up all animal products is not an effective way to make a difference. It's better to make an effort to buy meat that is free-range, organic, etc...because money talks. Unfortunately, I don't see this shift ever happening because many people either can't afford or just aren't willing to spend extra money on the meat they buy. tyflier also made a good point that ALL factory farming, including the mass production of plants for food, has a negative environmental impact. It seems to be kind of a no-win situation.