Short answer -- what you been told is essentially correct
Long answer, in United's
Contract of Carriage it states
REFUNDS - VOLUNTARY UA RULE: 0270
A.4) ANY APPLICABLE SERVICE CHARGE OR CANCELLATION PENALTY WILL BE DEDUCTED FROM THE REFUND AMOUNT IN 1) OR 2) ABOVE.
EXCEPTION 1: IN THE EVENT OF ILLNESS/DEATH OF THE PASSENGER/IMMEDIATE FAMILY MEMBER (TRAVELING OR NOT)/ TRAVELING COMPANION, ANY APPLICABLE CANCELLATION, REFUND, CHANGE FEES WILL BE WAIVED AND REFUNDS WILL BE MADE IN ACCORDANCE WITH THIS RULE. THE PASSENGER MUST SUBMIT TO UA A PHYSICIAN'S CERTIFICATE STATING THE CIRCUMSTANCES WHICH NECESSITATE WAIVER UNDER THIS PROVISION. ......
Which essentially says that your tickets can be refunded without penalty but UA does require formal documentation. What the agent said is likely correct given the timing of the cancellation. You need to cancel before the actual flight time and it will take some time to get the documentation to United. Once the documentation is received, they will refund the penalty.
also see
www.united.com > Services & information > Children, pets & assistance > Unexpected travel & itinerary changes >
Medical, personal and travel emergencies
Hope your mother gets better quickly.
further references
http://www.flyertalk.com/forum/unite...ad-merged.html
http://www.flyertalk.com/forum/unite...e-medical.html