JellyBean 91 and paperclip, it's pretty shocking some of the things that are deceptively unsuitable for vegetarians, right?
As for the "what defines a vegetarian" argument, I am not vegetarian so find it difficult to comment. But in my humble opinion, I believe that a vegetarian is someone who has decided to remove all meat products from their lives, and a vegan, someone who has removed all animal-derived products from their lives. This is obviously not a physical affliction, but rather a psychological restraint a person places upon themselves for whatever personal reason (and I see no problem with that), so if that vegetarian individual accidentally eats a Cornetto without realising it's unsuitable, they don't instantly stop "being" a vegetarian. But if they buy said Cornetto whilst knowing about the animal additives but think "to hell with it, it tastes nice", then that latter person is not really a vegetarian at all.
I would place that latter person in the category "picky eater", along with those infuriating individuals that say "I'm a vegetarian but eat chicken and fish and sometimes a burger but never anything else."