Fallen Firefighters Assistance Tax Clarification Act of 2013 - Treats payments made on or after December 24, 2012, and before December 31, 2013, by a tax-exempt organization on behalf of any firefighter who died or was injured as a result of the ambush of firefighters responding to an emergency on December 24, 2012, in Webster, New York, as related to the purpose or function forming the basis of such organization's tax-exempt status, if such payments are made in good faith using a reasonable and objective formula which is consistently applied.