Okay, so that would seem to imply that you can't open the fuel flap when the alarm is on, but having the flap open won't trigger the alarm.
I was thinking that the fuel flap could be a real stinker to try to identify as the location of a problem sensor, but I guess that's not it.

 

No, it won't trip the alarm. But if the car is locked and alarmed, the fuel door will not open.

Check your hood alarm switch and your tailgate - is it all the way shut?