What should go in an Italian Sub sandwich?
I know of three ways for a recipe to become standardized, and I doubt that any of them applies to your sub. 

The first one is: someone creates a recipe and is well-known enough for people to imitate him. Then it gets called the name he gave it originally. Example: Sachertorte. There is just one recipe for it, created by Franz Sacher, and any deviations are considered non-classic. I doubt very much that this is the case with your Italian sub, but there is a tiny chance that this is how it happened. It is what happened with "Italian beef" in America: obviously it is a known and imitated meal, at least in the Chicago area, but there was one restauranteur who started it, so you could say that his recipe is authentical. For more info on Italian beef, see http://www.youtube.com/watch?v=yevJMRceuvE&amp;feature=related (thanks to @hobodave for the link). 

Second, you have a case a well-known meal of unknown origin, which everybody prepares the same way. At some point, a name sticks, and nobody knows why. This is what happened to the Wiener Schnitzel. Even though it is a well-defined recipe, and undeniably Austrian, cook books listed it under different names until at least the beginning of the 20. century. The recipe has so little variation, you can be always sure what the real Wiener Schnitzel is. As you say yourself that there are many variations of an Italian sub, this is clearly not the case here. 

The third possibility is when a dish is prepared in many variations and there isn't a clear-cut name, but an established author comes along and codifies a taxonomy which becomes so popular that everybody starts to follow it. This is the case with French sauces. Even today, I know lots of people who confuse Hollandaise, Bearnaise and Mayonnaise. In fact, the stuff you can buy in a tube in a supermarket and is often eggless shouldn't be called mayonnaise at all. But since Carême wrote his work on French cuisine, and Escoffier elaborated it, cooks know that there is a difference a layman is often not aware of. This case supposes that there is a reference book recognized by the whole industry, and I am quite sure that nobody has written such a book on American cuisine. While I am sure that many have written books with such content, none has become influential enough to be considered canonical. So the Italian sub can't have become standard in that way. 

If you can find more on the origins on Italian subs, there is some chance that you will strike a nice story like the one behind Italian beef. But it is much more probable that countless sandwich places just put the two or three Italian-sounding ingredients they have lying around in a sandwich and call it "Italian". 

Oh, and to make it clear about the name: The fact that it is called "Italian" doesn't mean that it is a standard sandwich made in Italy. It is very common for food called after a country to be either totally unknown in the country itself, like this sub or Italian beef, or to be used for a single of many preparations known in that country - "Belgian chocolates" applies to a specific style of chocolate, no matter where it was manufactured, and you can find many different styles of chocolate in Belgium, the internationally known "Belgian chocolates" being only one of them. The sub sandwich is a very typical American meal, and while it is well-known around the world by now, giving one variation the name "Italian" shouldn't make you think that this is how Italians eat their sandwiches, or that all Italians eat their sandwich the same way, or that they have even heard about this specific sub.