They are gaslighting you, there’s no other way to put it. Why would there be a fare difference if they have to use the fare that was on the day you got ticketed? It was the same price. Unless you had your ticket already reissued in the meantime.

I used AMEX travel to book this and they didn’t even flinch when i told them i want the outbound changed. So there are cases when booking via OTA is actually better.