Virtually any restaurant can handle large groups. However, they must have the physical space available to be able to put the tables together. They may have the tables empty at the time you arrive but they may be scattered throughout the restaurant in a way that there is no space to create a table for eight. In that case, you will most likely be offered the choice of separate tables or to wait until a table can be created (they'll say available).
That's why the disclaimer. At restaurants like the one in our hotel, the wait may be 40 minutes in that situation, but at Disney, where the restaurants are much busier it may be as much as a couple of hours. But as people say, Disney is pretty good at avoiding the worst case.
However, don't worry about the restaurant, they can all do it.