This has been addressed many, many times. According to the official WDW site, you are not to rent a car, but send your luggage on DME. Now, in real life, there have been people that have done just that. They book DME, put the yellow tags on their bags, and then go off and rent a car to drive to WDW. Nothing bad has happened to them or to their luggage. But, and this is the sticking point....Disney would be well within their rights to stop transporting bags that belonged to someone who had not checked in and gotten on a bus. They have said that DME is not a luggage transfer service, that it is a 'perk' of riding on the DME bus.
So....at any time they could change over to a policy where you would have to checkin at the DME counter and then get on the bus before your bags were released. I would imagine it would be simple enough to do from a 'tech' point. Once you have been scanned getting on the bus, your reservation number would come up as 'clear' when the bags were scanned, and then the bags would be released to head to the resort.
This isn't in place now, may never be put into place. Just wanted to let you know. Can you imagine getting to your resort via the rental car, checking in and then waiting a day for your bags before you realized they were still at the airport? Now, that would not be a good start to a vacation. But, as of right now, that won't happen. Go ahead and do what you wish. I would suggest sending someone to get the rental car while the others are waiting for the bags at baggage claim. Then you will have your bags with you, rather than waiting up to 3 hours for them to arrive via DME truck.