I always thought QNE was used when landing at an airport with 1013.25 (ie SPS) set. Specifically, the QNE was the 'height' shown when the aircraft was on the threshold. I'm not sure that QNE refers to all heights read from an altimeter set to the SPS.
ie, with a sea level pressure of 1013.25 and a 'perfect' atmosphere, the QNE of a threshold 500ft above msl would be 500ft. If you were flying downwind in the circuit 1000ft above the threshold your altimeter would be reading 1500ft, but that is not the QNE.
Standing-by to be corrected!