Anyone who has DME reservations but doesn't have their DME luggage tags DOES NOT need to claim their own luggage.
Here's how to do it. Everyone who uses DME, EVERYONE, has to register at the DME Welcome Center at the airport. One of the questions they ask everyone is if they out the DME tags on their checked luggage. If not, they have a procedure in place. They ask for your baggage claim numbers, and also ask you to identify each checked bag, using a photo array of every piece of luggage known to man. With that information, they dispatch a Disney CM to go to the baggage claim carousel, claim your luggage for you, then take it "behind the scenes" and DME-tag it and put it with the rest of the DME luggage, which will then eventually be loaded on trucks and delivered to the resorts.
So like I said, not having DME tags doesn't mean you have to get your own luggage. PERIOD.
However, someone who doesn't have actual DME reservations can't use DME. Without tags, someone who's not in the computer system and who lacks written proof of such a reservation would be out of luck and wouldn't be able to use the free DME bus ride or luggage delivery.