All it takes is a man with a weaker denial than Clarence Thomas, or even Bill Clinton.
In Clinton's case, practice makes perfect. He is an accomplished liar.
HIs parsing of phrase and meaning when he made the famous statement "I did not have sex with that woman." while pointing directly at Helen Thomas, (who was likely on the short list), making a brief pause and scan of the people assembled before smirking and saying "Monica Lewinsky." as a non sequitur permitted him the gravitas and calm of not lying, but appearing to say something he really didn't. Textbook, and worthy of study.
I think with the media barrage on Thomas, he had more time to consider his answers and the questions he was asked, especially by Media personalities who were sympathetic and less hostile on more conservative shows. They did not want to feed him to Anita Hill and the Dems, especially with the sting of Robert Bork not so far back.
OTOH, Hannity (on the heels of so many Hollywood sex scandal/revelations) seemed adversarial, and may even have been hostile, and a former DA like Moore would pick up on the intent to catch him in a rhetorical trap early on. For that reason he would have to mull over the question, consider how an answer could be used to trap him later on in a misinterpretation by someone who was hostile, and construct answers which would be honest, yet not vulnerable to being twisted. You don't just go tap dancing in a rhetorical minefield. You just aren't going to come off as slick as a telemarketer under those circumstances.