@Bentwood0,
You mentioned your rate types, refundable and non-refundable. If the guest book a non-refundable rate, then she isn't entitled to any refund under any circumstance, unless it is an approved extenuating circumstance. However, you do have a flexible cancellation policy for those guests who choose to pay the regular rate. Since you received a refund request, it appears that the guest selected the non-refundable rate, and you were within your rights to refuse the refund request. If she had paid the full rate, you would have only received a cancellation notice.