I think you're missing a part on the inside. It's the one part that's hard to put back on, so someone may have not bothered with it. It's the L bracket mentioned in the first post here.
The black tab that moves with the key is curved on the end, but it goes straight out at 90° to the key to catch on the part that may be missing.
The lock cylinder and the black tab extend about 1" inside the ring. The part you need is attached on the back side of the ring and goes back about 1" to allow the black tab to catch on it after the key is turned to the lock position. Without that part on the inside of the ring, the black tab has nothing to catch on except for the inside of the ring. Without that 1" part, the black tab has to be bent way toward the key, like in your photo. It probably can't be bent far enough to touch the back of the ring when closed.
I hope I explained that right. You need that small 1" silver part on the inside of the ring to make it work right.
I think you could easily make that L bracket part yourself if you knew exactly what you needed.
Edit: I just found the part numbers for what you apparently need. Call an Isuzu parts dealer to see if they can be ordered.
Fuel filler lock hook- # 8-97164-850-1
Hook nut- #8-97068-819-0
Mark