Alex,
We may be arguing symantics but in this case symantics are important to the system fitted to the aircraft. The B737 NG cannot fly GPS approaches, only the FMC has access to the GPS unit, it is automatic and has no operator interface. It has no RAIM facility to check RAIM prior to flying a GPS approach (remember it is a requirement to have RAIM for a GPS approach, and please read to the end of the reply before hitting the keyboard). That is for a GPS only approach.
However the NG have a better system than RAIM for integrity and can fly LNAV/VNAV approaches that co-inside with a GPS approach, with GPS updating the FMC position and you are correct that the FAA has authorised approaches with a minimum of RNP 0.3 and with a few other riders if using the VNAV function. You are in essence flying an FMC approach, not a GPS approach.
Here is the difference, and it is important, with a non FMC aircraft on a GPS approach and a GPS failure occures a missed approach must be carried out i.e. you have had a navaid failure. With the NG and any other Boeing approved aircraft for LNAV approaches as long as the ANP is less than the RNP then the approach can continue. Symantic's maybe but it is a big difference.
RNAV, RNAV(GPS) and FMS are the interim generic term, as is RNP approaches. FAA, JAA, CAA etc are still discussing what to call these type of approaches and have still to come up with common charting and procedures etc, although GLS is the most likley at this stage. WAAS and LAAS are also to be intergrated as approaches. RNAV includes all sorts of equipment LORAN, VOR/DME (KNS88 types)
RNP approaches are still rare with only two RNP approaches Down Under so far but more on the way soon, and only Qantas 738's approved to fly them so far, with most in Alaska and Canada. Boeing are moving too only two type's of approaches very fast (ILS or GLS)
Things are changing very fast in approach technology and the 787 will push that even faster.
Fly safe and often
Regards P