I KNEW IT - there are two antennas. Remember, the 'halo' antenna is for RFID operation, it has to couple tightly to the chip in the key so as to not only 'talk' to it, but to power it up as well.

The transmitter in the fob for lock/unlock has it's own power source, so no tight coupling is needed. Also, MUCH greater range is required for the lock-unlock function, so an actual radiating antenna is used. (And after 34 years in the industry, the one thing I know, is radio.)