Both the Seller and the Buyer must sign the forms necessary to have your wishes respect and the sale price not show up in the MLS. If only l side signs, the forms are null and the price goes in. The Title Co you are using must receive these forms as they are the ones who do the Recording at City Hall.
It is shocking your Agent is upset. Her side of the sale will show up as representing the Buyer - but it will show the listing price. No big deal.