Randy Jackson encouraged an “American Idol” reject to hop up on stage and perform for a packed house at his guitar line launch. Jackson visited the MacDill Air Force base in Tampa, Fla., last Thursday to celebrate his new line of HSN “American Tribute” guitars. Spies said one female soldier told Jackson that she’d tried out for “Idol,” but didn’t make the cut. “It wasn’t me,” laughed Jackson, when she asked why she didn’t qualify. To make it up, the woman sang “America the Beautiful” onstage.