Lemma 1

If in our net we can find a "bad rectangle" then our net is not solvable. A "bad rectangle" is a rectangle with corners at blocked cells A,B,C,D where AB, BC, CD, DA all define a row or col, A and B are in a 3x3, C and D are in another 3x3.

Set ABCD = 1212. We can easily* continue this into a solved Sudoku grid. Now let's place our net on the board, covering ABCD (we'll assume that that is all it covers, since if the net covers more it can only make the puzzle more ambiguous). Since ABCD = 1212 is a solution, also ABCD = 2121 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.