In political terms, the only thing to do with this sort of smearing lie is ignore it, or you give it weight.
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You are exactly right. He has made this statement, and, now, he should not make any more about the subject. If he is asked, he should just remind the reporter that he has already commented and has nothing further to add.
The media, even those without animosity toward Sarah, would love to get a back-and-forth going here.
I hope he does exactly that, and he probably will - but I, for one, got his back on this if he does not or can not.