Good you brought this belief. I am trying to confine discussion of temples to historical facts ( or hearings ) and avoid mincing beliefs - not to overstep into other arenas. But this Amman is also known to settle legal battles in the Courts. Still there is a "Pradhu" system. You file an Affidvit in the Register maintained by the Koil Poosari. If your claim is legitimate, he will tell you when you will succeed. Otherwise fine you. (Fees rS.11.25 Ps). I have seen some judges coming to the temple! And we will denote "Ae Gowri Amman" as you rightly suggested.
When we are ready to seek answers to the right questions, we can call Dr.Kalaikkovan (RVAM), Kudavoil Balu (S.MAHAL), Rajavelu (ASI, Ch),Dr. Thiagarajan (History - Ariylr),Dr.Subbarayalu (Tanjai Univ) and Dr.Nagaswary (Retd.Archl) to enlighten us.