The list of restaurants is not always the same, so what someone had on a recent visit may not be the same as what you get when you go to Hilton Head.
We have always used our room key to show that we are staying at the Disney resort. I'm not sure if they would accept the DVC member card, since there is no way of knowing that you are currently staying at the resort...
You can always check into the resort early, even if your room is not ready, and then you will have the room key.