that?

Now indoors, ABC played this exchange from the interview in which Walters helpfully prompted Senator Clinton to agree that the Lewinsky story was "one more false rumor." The exchange:
Hillary Clinton: "He told me it wasn't true."
Walters: "Did you believe him?"
Clinton: "I did believe him."
Walters: "One more false rumor?"
Clinton: "That is what I believed, yes."
Walters: "Even as the late-night phone calls between the President and the intern were discovered and the logs of gifts and visits became public, Senator Clinton says she cross-examined her husband again and again, and still the President claimed nothing happened until just two days before he was to testify under oath about the affair. On Saturday, August 15th, your husband woke you up."
Clinton: "That was probably the worst moment that I can even imagine anyone going through because what he told me that morning was that he had not leveled with me or anyone else,...."

Could you tell me what 'that' refers to, please? Thanks.