You are close. A totally stubby are won't accept LSA type 3, 4 and 5 so the only way out is a default route, just as you said. A stub area, however, does accept LSA type 3 so routing WITHIN OSPF network occurs normally but will use a default route for EXTERNAL locations.
Refererences: Cisco Certification: Bridges, Routers and Switches for CCIES. page. 395
Doan