Shortly after Idol, Aiken was offered the role on South Park with complete anonymity. Enticed by the chance to play his actual sexual orientation without the world finding out, he jumped on the opportunity, and has played the gender-bending school teacher of Eric Carmen and crew since. Staff on South Park and any special guests are required to sign confidentiality agreements with very strict terms and excruciatingly high financial penalties should they violate the contract. Even Paris Hilton couldn't pay such a penalty. South Park producers wanted Aiken because they knew his voice would lend a special gay twang to Garrison that would set him apart from other gay characters in shows without the political incorrectness for which the show is known.
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The above write-up is entirely the product of my imagination and is in no way the truth (as far as I know). I'm just bored and having fun with the question and writing a parody article. I can hear the similarities between Garrison and Aiken's voice, but it doesn't seem similar enough to be the same. If Aiken says he isn't gay, speculation isn't going to change that. Thank you for the opportunity to BS while watching South Park.