The poster was complaining about a $35 fee claiming the CSR is ignorant.
It seems clear there is a TY fee imposed on top of the airline's own cancellation fee and fare difference. The TY points are also not refundable.
Based on the T&Cs posted here, I am not sure who is the one being ignorant.
May be if cancellation directly done with airline, there is no TY cancellation fee but then airline may charge a fee "to take ownership" of the booking which is not originally booked thru the airline direct. If the OP was not charged such a fee, he was lucky because my experience was, CO charged such a fee for "agency booking" before it would do anything on the ticket. Most of the CO rules / practice have been UA rules now based on what have been reported after 3/3.