It is OK for the police to lie to you. Police lie to suspects to get a confession. The only way to find out the truth is to hire an attorney. An attorney can make one quick call to the police department and get the truth. They can then advise you if it would be worth going to court over. It might be best just to pay the fine and get it over with but you need an attorney to find out the truth.
I live and work in Westport; where is this guy? I rarely come to a full, dead, 0 degrees kelvin stop at a sign. Stop signs are placed to enhance safety and expidite the flow of traffic. I check the safety aspects and then expidite - slowly.