"I'm sitting right here happy doing what I'm doing," Abdul said Wednesday when asked if she felt vindicated by a report last month by two law firms that found nothing to corroborate former contestant Corey Clark's claim of an affair with the former pop star.
Abdul did say later that "when you have a show this successful it's crazy we haven't had any more discrepancies."
Abdul, Cowell, fellow judge Randy Jackson and host Ryan Seacrest were in San Francisco for auditions for the upcoming season, which starts in January.
The judges also said viewers shouldn't expect every contestant to have a flawless background, and that a good scandal can keep the show interesting.
"Not everybody is perfect and I don't think we should be looking for perfect people," said Cowell, who routinely skewers "Idol" candidates he deems aren't up to snuff. Cowell also promised to be "nice."
The judges also praised former "Idol" winner Kelly Clarkson's transition to mainstream star. Clarkson recently won MTV awards for Best Pop Video and Best Female Video for her hit "Since U Been Gone."
"We're proud, we're happy, and it's nice that she remembers the show as well," Cowell said.
The judges said viewers should be prepared for plenty more contestants like William Hung. Hung's dismal performance of the Ricky Martin song "She Bangs" failed to earn him a spot on "Idol" but won him a cult following and spots on television ads.
The allegations that Abdul had an affair with Clark, who competed unsuccessfully in 2003, received nearly as much publicity as the Fox-TV show last year and led to an ABC special called "Fallen Idol."
Fox has since implemented a "enhanced non-fraternization policy" to prevent incidents that could call into question the relationships between judges.
Asked if a lack of distractions would make the season easier, Abdul looked at Cowell and Jackson and said: "It's never easy sitting between these two."