Quote Originally Posted by animus
I don't think Fire would be Shaolin. Air would probably be more likely as shaolin martial arts teaches to disable, and disarm your opponent and not to kill. And seeing as how fire is the most destructive element it'd go against their teachings.
There was a quick special during the commercials of one of the "movies" when it aired on Nickelodeon. They showed the guy they use for reference motion capture, and he explained that Fire was based off Shaolin, and gave a brief explanation.

You are right about the combat philosophy behind Shaolin, but the actual stances and moves of Fire Bending are straight out of Shaolin. It is the only one I was 100% sure on, since they outright said it.