Further to dusk2dawn,
DME ground stations have a built-in standard 50 microsecond delay between receiving the aircraft interrogation and transmitting the response. This is intentional, so the aircraft's DME transceiver "knows" about it and factors it in to the time-speed-distance calculation.
If you change the 50microsec delay, if will change the zero-DME point. For example, reducing the delay will cause the DME readout in the aircraft to be less than the true distance.
So rather than the DME referencing zero at the DME antenna itself, it will reference zero anywhere on the surface of an imaginary bubble extending around & over the DME antenna, a bubble which coincidentally intersects with the touchdown zone of the landing runway.
If you fly over an airfield and the DME reads a lesser distance than your altitude above the field (say, 0 DME at 4000'AGL), then you know that they've played tricks with the timing.