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.
Many people don't want the sale price posted. The method to do that is to instruct her of your wish and put it in writing. The brokerage needs your written instructions per the MLS rules. The agent will put the list price in the sold field with an asterisk. We all know what it means and if we are doing comps and your house is important enough we can call the agent and ask.
You might also be interested to know that sold information isn't accessible to the public from the MLS.
That said, having the sales price disclosed is helpful to the greater real estate market b/c it helps establish fair market values (appraisals) for comparable properties. Also, I think the tax record will eventually show your sales price anyway and that is where sites like Zillow get their information.
Before Zillow, sales prices were harder for the public to get unless they asked a MLS member or went to the tax records department at City Hall. Now, it's all out in the open, though often inaccurately.
Hope this helps!