A lot of the confusion in discussions such as this is the understanding of how each aircraft is configured.
In most airline original fit such a 'glass Boeings and Airbus' the GPS is just a sensor input to the FMS. It is the FMS that does the navigating not the GPS. As such it is the FMS accuracy and performance using all available sensor imports that is being measured and displayed to the pilot. The GPS derived position is added to the mix IRS, DME/DME, VOR/DME etc at a differing level depending the aircraft FMS design.
Another misunderstanding is that EPE, ANP etc is an error calculation. The question to ask would be if it knows the error why can it not correct the position! So all that the units can do is predict how accurate, based on a number of technical measurements and some statistical calculations the FMC is able to have "confidence" of it's Nav capability.
In GA world it is the GPS that is the heart of the navigation, so the performance of the system is totally dependent on the health of the GNSS system.