You're both right, the aircraft position as reported to aircrew, displayed on maps, and fed to the flight director (the autopilots outermost loop) is a blended INS/GPS solution. The opensource drone projects Ardupilot and PX4 have a lot of info and implementations of this actually.
However the autopilots inner loop and Flight Direction Indicator (artificial horizon) are going to be driven almost entirely by INS. This is because GPS positions can't update fast enough, are noisy, and don't provide velocity, acceleration, or orientation (outside of even slower position integration). Also those systems are not particularly involved in where the aircraft is, rather they care about where it is going.
I haven't looked into what the requirements of ADSB position information is, I don't suspect that they mandate GNSS but they may mandate a degree of accuracy. From an ATC perspective within crowded airspaces ADSB would be augmented by primary surveillance radar to prevent mishaps, spoofing, and errors.
For what it's worth my day job is aircraft avionics, navigation equipment is pretty much daily for me.
Ps. Hi HN, Reddit refugee and my first post here.