It doesn't matter. Let's call it a ground based receiver program then.
It plots your position accurately on a map, and you can zoom out and see the whole world,
or in the case of Google Earth, see your house.
The title of the thread should be map grid transformation, and therefore,
every shape on the grid also being transformed with the "corrected" projection,
and the user experience being that of observing another point of view,
even if only for entertainment. That's where I think the value is.
I don't think I can make anything that works without massive logical problems (surprise).
The existing program knows a lot about the spherical Earth,
and it would be impossible to make the two agree on everything.