In fact, if you ask people not from a CS background to explain the steps they would take to solve a puzzle, they probably wouldn't be able to think of a DFS, but they would state that they should rule out from each cell the numbers already present in its respective column, line and block. And for a Sudoku solver I don't think you really need more constraint propagation than that.
Anyway, I think you approached the problem the right away, I just think that you were so close to succeed in that test and it wasn't something that difficult to add to your solution.
EDIT: wrote the above before your edit. It's still appropriate though.