Big the story you linked to does not say that America is supporting that Sunni group. Did you read the story?
According to the U.S. investigative journalist Seymour Hersh, there?s another theory of who is really supporting the group: the Lebanese government itself, along with the United States. Last March, Hersh reported in the New Yorker that the U.S. and Saudi governments are covertly supporting Sunni groups like Fatah al-Islam as part of a policy against Iran and growing Shia influence in the Middle East.
In a recent interview with CNN International's ?Your World Today?, Hersh also said groups like Fatah al-Islam are the result of Washington's underground policies. He said an agreement between the U.S. Vice President Dick Cheney, Deputy National Security Advisor Elliot Abrams and Prince Bandar bin Sultan, the Saudi national security adviser, stipulated that the Saudi regime ?covertly fund the Sunni Fatah al-Islam? as a counterweight to the Lebanon?s Shia resistance movement Hezbollah.