@aterpster, i wasn't talking about RNP AR, just GPS/GNSS approaches. And yes, we do not need any GPS for those, nor for any RNAV approaches with more than RNP 0.10. You are correct however, for any RNP AR with RNP 0.1 or lower we do need GPS, if the RNP is higher than that and if DME/DME coverage is sufficient we don't need it again. Quite academic though as i haven't seen any complete GPS outage yet and since the NG does not have any RAIM requirement nor indication we do not need to care about that either.
Not quite sure what part of the world your rules are based but in my world:
RNP AR starts at RNP .3and requires operator specific certification to go below that to a minima of .11 for the B737CL and .10 for the A320. Dual GPS and Dual FMC mandatory for RNP AR
RNAV (GNSS): Ends at RNP .3 and can be Single GPS and Single FMC minimum with alternate ground navigation capability available for missed approach. With a Dual GPS/FMC ground aid not required.
RNAV: DME/DME availability required to be demonstrated as able to supply an acceptable geometric update for FMC
A stand alone aircraft GPS unit does need RAIM however with a GPS as a "sensor input" to an FMC equipped aircraft the FMC will calculate an ANP (Boeing) or EPE (Airbus) which will indicate the confidence in the calculation of a position.