Wow. Ok. I also called United as I posted this message. The CSR took some time to review and said if I cancel before 24 hours, no issue; but within 24 hours, and I might only get a credit but not a refund. Kind of sucks. Want to go with WineCountry's answer, which I thought made sense.
May be call again and also check?
I have had this happen (different answers by different CSR) in the past.