Are you nuts? The agent has not responsible regarding what appears on aggregate websites regarding your home. When you agreed to advertise on the 'internet' you, and your agent, relinquished all control regarding your homes information. ALL CONTROL>......FOREVER!!!!
And there are hundreds of sites that can do whatever they choose regarding your homes data, including, pretending its for sale......long after you remove or it is sold. If the details of your home, made available via aggregate website, causes a future owner harm...do you think you will be off the hook?
Real buyers rely on the MLS where control of your homes data is assured.
Those websites contractually participating with your MLS are held accountable for the data displayed. Yes, via most mls' the school district is searchable.
Aggregate websites such as Trulia and Zillow...can do whatever they please....because you said it's ok to advertise on the internet. Are you beginning to see the light?
Real buyers, those who are financially able and committed to buying a home, are working with a REALTOR and are making their buying decisions based on MLS data. There is no value to the homeowner in placing you home on the internet...only long lived liability.
There are other things you need to do, if this is a real concern for you. I don't think it is so I will go not further, You can however. read my Q&A and blogs and figure it out.
Outrageous indeed. Your agent should have advised you. Would you have listened?