I think it doesn't run when it's called from the grader since you have rows = [] and columns = [] defined outside of the procedures. I don't think anything which is not contained in a procedure is used.

If I try to run the code multiple times, since rows = [] and columns = [] doesn't get reset, it gives very mixed results. For instance, if I run
[[4, 3, 2, 1], [3, 2, 1, 4], [2, 1, 4, 3], [1, 4, 3, 2]] in isolation, your code returns True but if I run it after some others, I get False since on the second run through, rows and columns are equal to what they were at the end of the last run through.

Edit: Putting columns = [] under def check_columns(sudoku): and rows = [] under def check_rows(sudoku): should fix it.
@Angel's suggestion streamlines your code nicely (as having duplicate code is generally not a good idea as if there is an error, you have to change it twice).

I think you have your first example on the perils of global variables.

After you run check_sudoku on an incorrect sudoku, since then, the following calls to check_sudoku will return False though it is correct or not. For example:

print check_sudoku(correct)
print rows
print check_sudoku(incorrect)
print rows
print check_sudoku(correct)
print rows

You get:

True
[True, True, True]
False
[True, True, True, True, False, False, False]
False
[True, True, True, True, False, False, False, True, True, True]

Ups, the second time you call check_sudoku(correct) you get False. Why? Because of the global variable row that you did not reset to [] before append new elements. Your row variable contains all the elements from previous function calls.

My humble suggestion:

Try to avoid global variables. You could have those variables as local variables inside each method instead.

I'm not saying it's a bug, but... suggestion here:

def check_sudoku(sudoku):

    return check_rows(sudoku) and check_rows(zip(*sudoku))