The point about sidewall strength is a good one. Softer tires (like the S12) work fine in dirt, but will pinch flat very easily in rocks. A few tires that do have sufficient sidewall for the Adv are:
Dun 739 FAJ (the J is important)
Dun 755 (softer but great in mixed conditions)
I presume the Michelin Baja and Desert are stiff as well but have no direct experience.
The Kenda Millville seems to be stiff enough to work, but I haven't run one yet.