Items that are available without a prescription, but you get a prescription for it, ARE eligible for reimbursement from an HSA or FSA. (publication 969 pages 9, 17 and 19). I agree that items that don't require a prescription aren't eligible for the tax deduction according to page 16 of publication 502.
However, since §223 on HSAs relies on §213(d) for the definition of medical care, and §213 also controls the medical expense tax deduction, I don't see how both statements can be true at the same time and both be in agreement with the tax code. It can't be true that a prescription for an OTC item makes it eligible for HSA or FSA reimbursement but not the deduction.
(Separately, there is a provision in §223 that makes menstrual care items eligible for FSA and HSA reimbursement without making them eligible medical care for the tax deduction, so Congress and the IRS know how to split the two concepts when they want to.)
Therefore, while I am not a lawyer or IRS agent, I would argue that a prescribed item is eligible for the tax deduction, even if it is also available without a prescription, and particularly if it was prescribed for "diagnosis, cure, mitigation, treatment, or prevention of disease".
