The newer systems still use inertial as primary. As autoflight stated the newer inertial navigational system will position update via GPS, as well as DME inputs, when available. This corrects for position error throughout the flight.
Isn't that saying that GPS is indeed primary for meter-precision at north 60?
Not sure about other planes, but in the new Boeings the FMC calculates the most probable position and is more or less identical to what the GPSes say. The IRS position quickly strays as a function of time.
I am quite sure you can get unlimited MNPS approval with dual GNSS of correct type & installation. Smaller airliners and bizjets are normally not equipped with inertial navigation.