Yep, the article should be explicit about that. Calling American-Italian food "Italian" is incorrect, but also incredibly parochial.
Calling anything "Italian" would be equally parochial, as Naples, Milan, Sicily, etc have broad differences in cuisine and culture.
Along the same lines, when I tell my friends that I'm going to a Chinese restaurant, they know exactly what I mean. And no, it doesn't mean I'm taking the next flight out to Shanghai to eat.
It may come as a shock to you, but there are also Italian restaurants in other countries - not just Italy and America.
People should pick up on the context a bit.