Open Access to Courts Act of 2009 - Prohibits a U.S. district court from dismissing a complaint: (1) unless it appears beyond doubt that the plaintiff can prove no set of facts in support of the claim which would entitle the plaintiff to relief; or (2) on the basis of a determination by the judge that the factual contents of the complaint do not show the plaintiff's claim to be plausible or are insufficient to warrant a reasonable interference that the defendant is liable for the misconduct alleged.