A person eligible for benefits under this part shall be eligible for authorized physical and mental health care at U.S. Government expense (through either or advancement or reimbursement), and for payment of other authorized expenses related to such care or for obtaining such care for any illness or injury, to the extent, as determined by the Secretary of State or Agency Head, that such care is incident to an individual being held captive and is not covered by—

(a) Any other Government health or medical program, including, but not limited to, the programs administered by the Secretary of Defense, the Secretary of Labor and the Secretary of Veteran Affairs; or

(b) Reimbursement by any private or Government health insurance or comparable plan. In the case of coverage by a private or Government health insurance plan, that carrier will be designated as the primary carrier, and benefits under this subpart will serve only to supplement expenses not paid by the primary carrier.