China is not yet 'WGS 84' compliant. That means that the coordinates given by the Chinese authorities may disagree with GPS ones, hence the warnings. The recommendation is to disable GPS updates while in Chinese airspace, otherwise you will gat 'map-shift'.
Indeed so, the devil is in the details
Now, my experience with GPS is using it stand alone, not as an update feature with an FMS/FMC.
In my private aeroplane, the Bendix/King unit has proven unfailingly accurate as a primary means of navigation, indeed where the RNAV (GPS) specific approach course overlays a localizer, the course centerline of both is one in the same.
In large jets, the Honeywell HT9100 GPS units have been approved for ten years for stand alone primary navigation, enroute/terminal.
Superbly reliable kit, in my personal experience, in Europe/USA/Africa/South Asia.
Now, I'm certainly not saying GPS can't fail, just that it is extremely unlikely, from my personal experience.