Can not believing a false statement qualify as knowledge?

No.

However, what leads you to believe or disbelieve a statement could be knowledge.

Consider, a weak candidate is set a multiple-choice paper on which there is a question with four answers.

The candidate doesn’t know the correct answer, but he knows that answer C is incorrect, because he got laughed at in class for offering that answer previously.

Instead, he chooses a different incorrect answer, for which he scores zero points.

The reason is that he displayed zero knowledge in that question.

Do you feel the candidate should have got at least some credit for knowing that C was incorrect?

Perhaps that’s fair: at least he knew it was incorrect.

But now consider a candidate who disbelieves answer C because someone has previously told him that all the C options are incorrect. He doesn’t know the correct answer, but he does not believe it is C.

In this particular case, he is right, but, in reality, the person who told him that was just playing a trick on him. Even if he happens to choose another answer correctly, his refusal to pick C is not based on knowledge, but on lack of it.