I am vegetarian and I eat so little eggs, cheese or milk that I am leaning toward vegan. I think many vegetarians do consume dairy products. I think the issue is that you are confusing vegetarian with vegan.
I am not a member of PETA. I do agree with their cause, but I don't agree with their ways. When I do eat eggs, cheese or milk, it comes from the small farm of a neighbor across the road. I see how he treats his animals, and I've yet to see him mistreat any. I know that they planned on slaughtering one of their cows, and they backed out because none of them had the heart to do it after getting close to it day after day. I think that is the problem with the big farming industry that has taken farms away from farmers. It is even hard nowadays for a small farmer to make money from a corn crop.
So I don't agree with PETA entirely on this issue, but I understand their point. I don't see where they have those exact words on their website, but they do have plenty of articles stating that it is morally wrong to support the abuse of dairy animals. I believe it depends on the person and where they get their dairy products.