Check out the other instrument procedures in place for the airfield - that would give you a pretty good clue.
For example. If the airfield has an ILS/DME and also an NDB/DME check the small print. If the NDB/DME is not available without the DME element then it's a big clue that it's independant operation (You'd be daft to have to lose your NDB approach if you had the ILS off for tech reasons). If however there is a timed element available to the approach it's possible that the DME is tied to another facility, and as such they've taken the 'failure' scenario into account.