I'm assuming here...so take it for what it's worth (and I'm sure a DVC expert will answer you shortly... ) BUT, since DVC members are entitled to using the ME services, you should be too.
I imagine that the DVC memeber booking your reservation will give Member Services (MS) your flight information and will mail the luggage tags out. I'm just not sure where MS will send the tags...your address or the members?
Hmmm....maybe a DVC veteran can help us further....
I just had a thought about renters. Wouldn't the member have to call/book the DME through MS? Is there a generic number to call to book DME? I would think as long as you have a reservation number you can book through CRO.