Wrong. I first heard about the Seven Fishes dinner from Italian-American friends in college, and have since seen it described as a universal custom in English-language newspaper articles, some of which go as far as to attach a particular significance to a course or number of courses.
But it's not; in Tuscany, for example, those who observe the Catholic custom of avoiding meat on a Vigil will eat fish, but there's nothing that says one must, and Artusi, who gives all sorts of menus, including one for Christmas Day
, doesn't say anything about Fish on Christmas Eve.
In other parts of Italy people do eat fish -- because of the Vigil, and Naples is especially well known for its Christmas Eve fish dinners
-- but again, the number of courses and the kinds of fish served depend upon the number of diners and the depth of their pockets. There are no hard-and-fast rules.