Mozzarella: The Forgotten Vegetable

When you travel through different countries and cultures, you learn many things. One tidbit we picked up from a waiter in Salzburg was that mozzarella, contrary to our ignorant North American thinking, is not actually a cheese. My dad, who has a cheese allergy, ordered a pizza without cheese. The waiter, who appeared to speak adequate English, repeated the order and went off. He came back later with a pizza, covered with what appeared to be cheese. When we questioned him on this, he assured us it was not.
"That's mozzarella," he explained.
As this did not satisfy us, he explained further.
"Mozzarella is not a cheese, it's a vegetable," he said.
Eventually, we sent the pizza back with orders to get a new one "without the white stuff."
It's not clear what the mixup was; Dad thinks the waiter confused "mozzarella" and "mushroom", while I think he was just really, really bad at biology.
-Jason