If you're sure the fare rules specify a $0 change fee, pay what the agent quotes and ask Refunds to fix it.
Alternately ask the agent what your fare basis is and could they please read you the PENALTIES portion of your fare rules (doesn't UA show full rules online now?). If they don't know how to do that, send @
UNITED a tweet (hi, just talked to a phone agent who quoted a bogus change fee and seemed unable to read fare rules), and call again.