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Peggy can get away with false solution #1
(x-posted from my comment on Hacker News)
Suppose that in a puzzle there is only one 1 and one 9 that do not overlap in any way (row, column, or 3x3 square). Now, suppose that Peggy comes up with a false solution to the problem which sets both of these tiles to 9. Then, neither the 1 nor the 9 can be picked for the green squares, and so no test of Victor's can disprove Peggy's false solution.
This seems easily fixable too: rather than the whole green tiles thing, just allow Victor to query either a row/column/3x3 to prove the solution is a valid sudoku, or query the original filled in tiles, to show that the solution corresponds to the original problem.