I wasn't planning on answering here but since someone mentioned my paper in the long comment thread above maybe I should anyway.
When I'm solving problems by hand one of the sets of patterns I frequently use involve uniqueness: something can't happen because it would lead to a puzzle with more than one solution, but a well-posed Sudoku puzzle has only one solution, so it's safe to assume that whatever it is doesn't happen. For instance, it's not possible to have four initially-empty cells in a rectangle of the same two rows, the same two columns, and the same two 3x3 squares, and also for these four cells to all contain one of the same two values, because then the two values they contain could be placed in two different ways and the rest of the puzzle wouldn't notice the change. So if there's only one way to prevent a rectangle like this from forming then the solution has to use that one way.
I have the sense (though I could be wrong) that this sort of inference does not imply a unique rational solution. But of course a puzzle could have a unique rational solution anyway — my computer solver knows these rules too, but uses them less frequently than I do by hand.