Good Morning. Unfortunately, DVC does not qualify for free dining. However, you can purchase discounted AP passes and then get the TIW (Tables in Wonderland) card that can be used for 20% off food and beverages (alcoholic included) at a lot of places. You can also pay for the dining plan OOP. In May, when we are at BWV, we are going to get the QSDP and they use the TIW card at the two sit down meals we are planning. Hope this helps.
OP - you're not alone in your confusion. We hear this one quite a bit. I think people new to DVC often get confused in the difference between a resort hotel stay (which are frequently given promotions such as % off, or free dining etc) and a DVC (timeshare) stay.
As owners, we've bought in. Our rooms are paid for, we pay yearly maintenance dues to keep the DVC up to par. DVC units would be a whole different creature from the resort hotel rentals except that Disney chose to plunk DVCs down in resort hotels and some of the DVC rooms are owned by Disney, and they may choose to rent those like any other resort room (at outrageous rates) ... smudging the lines and confusing the newbies.
As others have said, no we don't qualify. If the software ever did accidentally add free dining to our stays I'm positive it'd be revoked as soon as they discovered the error. I'm not complaining - my kids and I don't eat out a lot, we dine our own way, using our kitchen/ette & DVC compliments the way we vacation.