The GPWS is valid, but because some approaches are 2.8 degree (due hot weather), if it is cold and with enough barometric error you are actually low on path compared to the ILS.
If this is true it sounds scary. I've not flown RNP approaches, nor an Airbus, but any IFR approach system that brings you below the ILS GP sounds dodgy to me. Please give more info.
As well as the Gringo event remember the Air Inter A320 at Strasbourg that made a smoking hole on the rushed VORNPA. Due to various nuisance warnings Air Inter had disabled the GPWS systems as it was not yet mandatory, only advisory. By not selecting the ILS you remove the "Below G/S" alerts. As I've mentioned previously, a/c have been designed with back-ups in nearly every system, including 2 pilots, but when on approach to terra concrete SOP's can dilute you down to only 1 nav system. Seems to go against the basic philosophy of back-ups and needs justifying by the SOP scribes. It reminds me of one operator who removed the SBY ILS from their approach Cx list. Why? I've no idea; and indeed no-one ever published why. The result was that some captains taught that it was no longer necessary to select it ON during approach. OMG. Trained monkeyness gone mad.