I'm no technical expert, but as far as I know in the UK, an airfield with ILS on both ends of its runway which both operate on the same frequency (transmitters being interlocked so only one transmits at any time) has a single DME which is adjusted so that instead of reading zero at the transmitter, it reads zero at each touchdown point, hence it's centrally placed between GP aerials. Course if your ILS has different frequencies at each end, then you'll need two DME's as well as they'll be 'frequency paired'.
Sorry if it sounds complicated, but although you obviously need LLZ and GP on both ends, if they're the same frequency you really only need one DME. Maybe it's airport operators economising.