Yes, annoying and really freaked me out first time. I can imagine that the computer is told to never increase the displayed fuel level while engine is on. One way to test this would be to fill it up with the engine running and see if the level responds in real time.... but I'm pretty sure thats a horrible idea and you should never test it. Like the bezel on a dive watch that can only be moved to show that you have been underwater longer than you actually have been, the one way fuel level movement may be "on purpose" to help prevent running out while driving up a large incline?? Pure speculation.
There's nothing wrong with leaving your engine running while fueling up safety wise. It can cause check engine lights on some cars though. Those stickers you see at pumps are just government nannie crap. Now, the no smoking stickers, yeh those are legit!!