It wasn't on the show. It was shown behind the scenes. She was booked to be on the show the week Chicago was shut down by a blizzard. The staff was making arrangements to get all the guests in town to make sure they could tape all the shows. Jennifer was in town for rehearsal, and then left for Dallas, unknown to the Oprah staff. She got stuck in Dallas and could not get back to Chicago in time for her show's taping, so they had to delay it, making the audience wait a few hours. During the whole think, Jennifer's staff kept telling Oprah's staff things that turned out to be untrue, like she was flying private and would do hair and makeup on the plane, when she actually flew commercial.
I think the issue with Jennifer wasn't so much maturity, as it was an example of what happens when fame comes to you so quickly. When a person has to work hard for years and years to get famous, they tend to remember what it takes, who got them there, and look out for the way they treat people. When a person is thrown into fame faster, through a show like American Idol, and skips over many of those long years of hard work, I think its easier to take the fame for granted. I think the diva-like behavior comes from thinking it all came easily, and she can behave like she wants because she's a star.