Asked by US chat show host Jay Leno whether the pair get along, Adam said: "They fabricate a lot of that – a lot of that's reality television fodder.
"She's fine, we bicker like brother and sister."
Christina recently explained her role on the show – which offers a $100,000 recording contact to the eventual winner – is about providing positivity and being "completely involved" with the acts.
She said: "There is no good and bad. This isn't about tearing people down. I want to bring these people up.
"We're looking to get more involved with people starting out just like we did. We're not just making commentary and then going home. We're getting completely involved. I wish there was a show like this when I was starting. I'm ready to share it all."