Okay, found the problem in the Change Notes for 4.1 (API Level 16):
android.database.sqlite.SQLiteClosable
implements java.io.Closeable
only from API Level 16. Before that, they were unrelated (even though both interfaces existed since the beginning).
So you should use SQLiteClosable directly if you want your code to be backwards compatible.
It is also probably worthwhile to install the SDK for the lowest version you want to support and try to build with it, then this would have been detected by the compiler.