That's probably right, Fernet with Coke is a kind of national drink, especially in the province of Córdoba, where everything suggests it was invented.

If you order a Fernet in Argentina, it is assumed that it includes Coke. Nobody that I know of drinks it alone, and it sounds weird to us to do that.

In the movie "The Dark Knight Rises" there's a scene in which Alfred goes to Florence and drinks Fernet Branca alone. The comment from many Argentinians was "What? No Coke? That's gross!".