Answer is in insider blogs.This is the best one, from an LA Times blog:
Who's That Girl?
Wed., Mar. 21
First things first: Who was the crying girl? After the show, I chatted with Idol’s newest superstar, the crying girl, Ashley Ferl, aged 13, from Riverside. For some long minutes after the show, Ashley remained in a state of inconsolable sobbing, unable to choke out a single word. However, through an interpreter (her mother) we were eventually able to learn some facts about the young superstar.
The family, I was told, obtained tickets on a website to attend a taping of “Smarter Than a 5th Grader” a day passage that included not just the taping of the show itself, but also the dress rehearsal of either “Grader” or “Idol.” The fates were kind, and the mother and daughter found their way to the “Idol” rehearsal, where Ashley’s waterworks began. Her prowess was quickly brought to the attention of “Idol” producers who summoned the clan to a ringside seat of honor at the final taping.
Her powers of speech slowly returning, Ashley revealed that while she was on stage she had been thinking that “this was the coolest thing ever.” Asked whom she was supporting in the competition she named “Sanjaya, Melinda, Gina and Jordin” as her picks, refusing to narrow her vote down to a single choice. All my journalistic powers of persuasion, cajoling, bullying and insistence that on her vote might turn the entire competition, that “Listen to reason, young Ferl, there can’t be four American Idols,” would not convince her to name a single favorite. To my every argument, she would only repeat her mantra, “All Four: Sanjaya, Melinda, Gina and Jordin.” And so the race begins in earnest, with tears at every step of the way.
The producers did know about crying girl and put her in nice seats so they could focus on her, but it seems like she REALLY WAS CRYING !!Crying girl is not a fake !! Long live Crying Girl !!

"A new broom sweeps clean, but the old broom knows the corners" - Martin, First loser on The Apprentice LA
They spotted a young fan that's soooo excited that she's completely losing her mind -- so they give her the time of her life by inviting her to the show...and get some good camera shots out of her.So what? It was good TV - got us talking, right? And little chick was having the time of her life. I just hope she didn't wet her pants.
There's a world of difference between that and planting a child actor to create commotion....no way did they do this. Why would they need to? They could probably fill the theater with little girls like that if they looked around a little bit.
(btw, it goes back further than the Beatles too - there's old film of girls in the 40's losing it over a very young Frank Sinatra)