They release some of their seats to Disney for the reservation line, hold some back to reserve directly at the phone number mentioned above, and keep some for walk-ups. When they first opened, the number was 25%/50%/25% but they may have adjusted it since. So yeah, if there's no availability from the Disney dining line or website, try calling directly.
With the Disney Dining Plan becoming more widely used, reservations at Disney Restaurants are hard to come by. That has affected non Disney Restaurants as they are not as busy. We were there over the Christmas holidays and were able to walk into both Rain Forest and T-Rex without reservations and the places were half empty. Talking to our server, she said that the Disney Dining Plan has really affected their business.