He might have been exaggerating the performance of his friend's "invention", but you can track the sun during the day, stars at night, and possibly other celestial bodies during the day with sensitive enough instruments. If you can calculate the angles between local gravity, the height of the sun, and you know what time it is, there is a lot of location information there, especially if you track changes over time and not just instantaneous.
I think all you need is two celestial bodies and local gravity to get a fix on your location.
Don't forget that the surface of the sun is not perfectly uniform: if you have a recent picture of the surface of the sun and sensitive enough instruments, you can effectively treat it as a "cluster of known celestial objects" (e.g. sunspots, solar flares) half a degree apart from each other.
Also the moon is sometimes visible during the day, and since the topography of the moon stays constant over time that trick will work with the moon (with craters etc) even without a recent picture.
I think all you need is two celestial bodies and local gravity to get a fix on your location.