Lemma 2

If in our net we can find two "bad rectangle"s each with one corner missing, and they share that missing corner, then the net is not solvable.

Let rectangle 1 have corners A,B,C,X and rectangle 2 have X,D,E,F. Set ABCFED = 121212. We can easily* continue this into a solved Sudoku grid. Now let's place our net on the board, covering ABCFED (we'll assume that that is all it covers, since if the net covers more it can only make the puzzle more ambiguous). Since ABCFED = 121212 is a solution, also ABCFED = 212121 is a solution, because in all units (rows, columns, blocks) involved we simply swapped 1 and 2 and thus nowhere did we break anything.

* axiom.