5LY:
Modern transport jets navigate using FMC position info. The FMC looks at IRS pos., radio pos. (by auto tuning VOR's and DME's) and GPS pos. and derives it's pos. by comparing all info and choosing what it perceives to be the most accurate. This is almost always GPS pos. IRS's drift, VOR's and DME's aren't always in range.
That isn't the case with some of the smaller aircraft he included in his question. They may have only a flux-gate compass and a Garmin panel navigator.