But the mineral water and the salad don’t necessarily need to be labeled as vegetarian.

I think the issue is that people don’t interpret the ‘vegetarian’ label on the menu as “this is OK for vegetarians to eat”, they interpret it as “we altered this dish to make it suitable for vegetarians”, and usually the latter means it’s not very good.

I don't think he implied otherwise. It was an opinion in reference to the study, which I agree with. If I'm at the store and grab a random snack off the shelf to try, I'll pretty much always put it back if the label says vegan because I've been burned by overpriced vegan snacks that taste like garbage so many times.

I don't follow. Salad is on the menu because salad tastes good and some customers like the taste.

Salad is not at all like an animal-based meal having its animal component replaced with something else.

Likewise, mineral water is there because some people like drinking water and not alcohol or soda.