As 172_driver stated in a nutshell.
The entire concept of PBN is that it is the performance of the system not the components of the system that is important.
ANP less than or equal to RNP is really all that is required.
In relation to the OP question the of the DME MEL. My take is that a second FMC would via scanning DME or agility tuning (as fitted) would still meet the RNP, however a backup for a missed approach may be required be that RADAR or Dead Reckoning.