Unless my car is different, this is how it works:
Situation A: CAR IS UNLOCKED:
You do not need the FOB to open the fuel filler door. Anyone can open your fuel door and siphon your gas if you leave you car unlocked.
Situation B: CAR IS LOCKED:
The fuel filler door will not open, even if you have your FOB within 31" of the door. Unlike the rear trunk release and the exterior door locks, the fuel door is not a proximity switch. Of course, you can use the FOB to unlock the car, but then you are in Situation A.