Let's get a couple of things straight here.
1. Are you based in Australia? It would help if we know who we're dealing with.
2. That text DOES NOT APPLY to Australia (not that I can find in our AIP, anyway!). Where'd it come from? Alpha Centauri posted the Australian AIP reference that covers this exact issue.
So…. now the only question I have is again…. in absence of a procedure to fly, which one would you legally be required to fly? I still say it is wise and prudent to ask for clarification.
Nothing in particular! Fly whichever ILS you like; they are both exactly the same (the DME used is irrelevant). The initial replies from ATC indicated that. I suspect that he finally caved in and gave you an answer that wanted to hear.
If we get every man and his dog now asking which one to fly because of this I'll spew...
