It's probably the antenna driver circuitry that's bad and not the antenna itself. All Nissan dealers have at least one "required" special tool for checking whether a fob transmits or not, so I'm sure they simply put yours on the Tech-II or the fob checker and found it wasn't transmitting. The "emergency start" circuit using the button is a completely different function that uses RFID and will work even with the fob battery removed, so a blown transmitter won't prevent that from working.