In Editorial of this question it is stated that “Once we have checked all rows, we check to see that every two-X row’s set of X columns pairs up with exactly one other two-X row’s set of X columns, and that no such pair shares any position with any other pair.”

My question is that since number of X is exactly 2*N-1. Why doesn’t it just sufficient to check that all row and column except one particular row and column should have exactly 2 ‘X’ and that exceptional row and column should have only one 1 ‘x’ ? Where does this logic fail??