Aviation use of the GPS satellites uses the unauthorized user signal. Therefore the US have the ability to 'shift' the data sent to your gps receiver and so your receiver thinks it is somewhere else (try using a civilian gps receiver in Iraq right now).
In response to back ups for VOR and DME etc - they do monitor themselves and if in error will switch off - you know they've done this as you lose the ident of the facility. There is no such ability for you to check the integrity of the satellites you are recieving. Differential GPS can assist in precision approaches but this is not available over here. GPS is approved for RNAV in europe but again must only be used in conjunction with raw data monitoring of the aircraft position.