McGrath of Harlow told us:

"Rebut" means to prove that some allegation is untrue. Just saying it is not true is not a rebuttal, but when it gets described as such people are liable to tricked into thinking that the charge has in fact been rebutted, or disproved, when in fact it has just been denied.

Au contraire, mon frere!

I think you are confusing "rebut" with "refute", which indeed means to disprove. Rebuttal is that phase in a trial or debate in which the party having the burden of proof can come back after the defense case or argument and attempt to shoot holes in the defense. Usually the scope of rebuttal is limited to new matters brought up in the defender's case or argument. The rebuttal may or may not be successful in refuting the defense, but it's rebuttal just the same.

Dave Oesterreich