Denti:
DME/DME updating alone (without GPS updating) is enough for approaches down to RNP 0.3, at least we were certified for that with our old -300s without GPS updating. So i guess switching it off is probably only required below that, however with certification for approaches down to RNP 0.15 for RNAV approaches and down to CAT I for GPS/GLS approaches we do not have any requirement to switch DME/DME updating off. Usual ANPs with DME/DME enabled are 0.02NM.
The U.S. stopped allowing DME/DME for conventional RNAV IAPs after a couple of serious incidents where the DME geometry was poor, at least at final approach altitudes.
Conventional RNAV procedures indeed use RNP 0.30 alerting and integrity, but unlike RNP AR there are wider primary obstacle protected areas, as well as secondary areas.
In an aircraft certified for RNP AR, DME updating should be automatically disabled anytime an RNP AR IAP is activated.