JABBARA,
When the chart reads "DME reads 0 at threshold", that is because the DME is located at the threshold. No DME that I know of has the means to "electronically" reposition itself, the DME reading will always be with respect to the the correct geographic position of the DME site. Consider an ILS/DME, the Localiser is at the 'Far' end of the runway, the Glide Path transmitter at the touchdown point, and, ideally, the DME is abeam or very close to the touchdown point, hence Zero reading at the threshold.
If you examine the FMC navaid data-base, you will see 2 locations for the one ILS/DME ident, one for the localiser, and one for the DME (The Glide slope transmitter doesn't rate a mention, as no position updating occurs from the Glide Path signal).
There is no need to inhibit the DME portion of the ILS/DME for DME-DME updating. You may continue to use the DME with confidence.
Regards,
Old Smokey