There are two completely separate sets of room inventory for the DVC resorts. Disney owns a very small (< 10%) pool of inventory of the sold-out resorts, and those rooms are made available to the public for cash reservations if they're not being used to swap out for rooms being refurbed or having maintenance issues. That's generally what you see available on Disney's reservation site. You'll also see inventory for the newer resorts that DVC hasn't fully sold yet.
The much greater portion of the inventory is owned by members, and non-members never have access to that pool of rooms. That's why it's not really correct to say that members get first crack at the DVC rooms. Members can book the inventory they own, the general public can book the inventory that Disney owns.
(Note: There are some very specific situations, as
@Marionnette mentioned, where member inventory can move into Disney's inventory. When a member exchanges out of the DVC system for a cruise or other vacation, DVC gives a room of comparable value to Disney to book for cash, which is used to pay for the member's exchange. Also, at 60 days out, DVC gives unused member inventory to Disney to book for cash, and that money comes back as breakage income to the resort.)