I can verify the above objection.

What about this board? Your solution says it's finished, but it clearly isn't.

[[1,2,3,4,5,6,6,9,9],
[4,5,6,6,9,9,1,2,3],
[6,9,9,1,2,3,4,5,6],
[2,3,4,5,6,6,9,9,1],
[5,6,6,9,9,1,2,3,4],
[9,9,1,2,3,4,5,6,6],
[3,4,5,6,6,9,9,1,2],
[6,6,9,9,1,2,3,4,5],
[9,1,2,3,4,5,6,6,9]]

I can imagine that, but in that case, some row/col/square must then fail the test in another part right?

There are situations where the sums of the elements of a row/col/square could be 45, but the numbers to reach 45 are not unique (2,2,2,4,5,6,7,8,9). For some reson my first thought is that these would slip through on squares the easiest.