UA may well respond that it's e-ticket receipt complies with a strict reading of the applicable rule, 14 CFR Sec. 399.85(c)

On all e-ticket confirmations for air transportation within, to or from the United States, including the summary page at the completion of an online purchase and a post-purchase email confirmation, a U.S. carrier....The fee information provided for a carry-on bag and the first and second checked bag must be expressed as specific charges taking into account any factors (e.g., frequent flyer status, early purchase, and so forth) that affect those charges.

In OP's situation, the e-ticket receipt specifies the fees, e.g. $0, but then explains that those take into account a FF status.

I would still try the refund route and might complain to DOT, but would not spend the refund until it is in hand (which might never happen).