Union Tax Fairness Act of 2013 - Requires that the payments to an applicable reinsurance entity for any plan year beginning in the three-year period beginning January 1, 2014, required under the Patient Protection and Affordable Care Act be applied equally to all health insurance issuers and third party administrators (on behalf of group health plans). Prohibits such payments from being waived on behalf of any such issuer, administrator, or group health plan.