Greenblatt didn’t identify as Israeli, he implied that he is part of the “Jewish nationality”, the fake conception of Judaism invented by Zionists. They typically avoid exposing their allegiance to this invented nationality, which is why he corrected himself to say Israel’s national anthem.
The key to debunking Zionism is to understand that it’s fake, but most people (including most Jews who aren’t religious) are enchanted by the mythology that Jews are something other than a religious group.
Mike