You're right, but also very wrong if you are using this to dismiss my obvious facts.
Vegetarianism is a DIET.
Veganism is a PHILOSOPHY.
Vegetarians are not necessarily vegans, but vegans ALWAYS have a vegetarian diet.
So the person in question could have worn leather or used products that exploited animals, but they will still be eating a plant-diet.
You see now why I say you are both correct, but would be incorrect if you dismissed anything on the account of being correct.
It would be the same as saying "The sky is blue, so you are wrong."
It follows that the sky is blue, but that does not necessarily mean we should dismiss any of the obvious facts of the argument.