Thanks Pete-zza, as complete as it seems, I think it must certainly be in there. For convenience, I'll quote the relevant paragraph.
Oil serves many purposes when used in or on pizza dough. When used in the dough, it coats the gluten strands, which helps improve the rheology (flow) and plastic qualities of a dough, making it more extensible (stretchy) and easier to handle and shape. The oil in the dough also helps to prevent moisture in the dough from evaporating too quickly, thereby resulting in a more moist crumb in the finished crust. If the oil is also accompanied by a lot of sugar, which also helps retain moisture in the dough, the finished crust and crumb will be soft and tender rather than crispy. These are characteristics that you will find in an American style crust, such as the crust of a Papa John's pizza. The oil in the dough also adds flavor to the crust. When the oil is used on the dough, it has good thermal transfer characteristics. This is what creates the "fried" crust effect when the oil is used, especially in large amounts, in a pan or disk that is used to bake the pizza. When the oil is used on top of the dough, it helps improve top crust color but it also captures and retains the flavors and "juices" of the toppings as they cook. Of course, oil also contributes to mouthfeel, which is a characteristic that people generally like.
I suspect that the first point might be it. In fact I imagine that "It makes it stretchy" might have been an acceptable answer. But then again, LC (as rumoured by some here) does tend to have long shelf lives for their dough balls, so maybe the moisture retention angle has legs.
I guess I'd have to throw out the "fried" crust (although they do seem to use this on their pan pizzas), and crust-color aspect - since the question was specifically about "in" and not "on" or "under" the dough.