I think the iPad's GPS is just to find a nearby waypoint as a starting point for the automatic approach and landing. Once you have decided upon a route, it's a simple matter of tuning the aircraft's nav radio to the VOR or ILS. From there, you have the full precision that you would normally have on an instrument approach/landing. The innovation is that the passenger doesn't have to know what an instrument approach is.

(I wonder if the code on the iPad gets the audio stream from the radio so that it knows it's tuned to the right channel.)

As an aside, I've read on the X-Plane forums that X-Plane doesn't actually do a full simulation as you say it does. If you try to spin the default C172, for example, you can't do it, because the aerodynamics near the boundary cases are not calculated correctly. (Either that, or the spin recovery for a C172 consists of letting go of the controls and waiting, which is not what the manual says. But I have not tried it.)