I think you maybe a little bit off here. If the yellow tags are not on the luggage and it gets to the airlines office the passenger will be responsible for the bags, unless the passenger goes to DME and actually gives DME the luggage coded numbers. The CM's do not try to match names of the DME manifest, mainly because they probably don't carry an up to date one and also the lists may be to long, to the luggage that is not claimed off the carousels. If you say you are going to pick up your luggage and do not put the tags on the luggage you will be responsible for it until you give your luggage coded numbers to DME. Than and only than will they pick up your luggage from the airlines unclaimed luggage at the airline office.
DME cannot pick up luggage based on names. There might be two or three passengers with the same name and all the luggage would end up at Disney. They need the coded luggage numbers to pick up the luggage.
The CM's do stop by the airlines offices and check to make sure they have got all the luggage that have the Disney tags on them.
One airline, Delta, has verified the only pieces of luggage that is picked up by Disney CM's, at the airline office, are those tagged with the Disney tag and missed by the CM's. They will pick up untagged luggage if they have the coded numbers given up by the passenger at the DME welcome center.