Refute/Rebut -- we should get it right

How difficult is it to remember the correct usage for refute versus rebut?

Very difficult, apparently, for The State newspaper, which consistently makes the wrong choice.

Rebut means simply to present a counterargument. Refute carries a much greater weight, the connotation that someone has proved the point.

Nothing could be further from the truth in this story, where the referee's story is being disputed even by the NFL's VP of officials. So the referee "rebuts" but hardly "refutes."