Hi, welcome to JustAnswer!. This is Ed.
Ultimately... you're right. The same grounding point is shared between the pump and the level unit, so if the pump works, the main ground is good.
Chances are heavily in the favor of a worn out level unit instead of a bad ground, but it does warrant a check... especially since you're already in the area.
Find and test the black/ light green wire of your pump unit connector for good continuity to ground. It should be 5 ohms or less if OK.
The signal wire (dark blue) is a pull-up voltage that's sent by the instrument cluster and while I'm not quite sure of what it should be...there should be something there with the key on. It could be 5v or it might be battery voltage. The point is that it should have something on the circuit. Zero volts at this point indicates either an instrument cluster failure or a wiring problem. If you happen to have either a perfect 5.0v or a reading equal to battery voltage on this circuit, it strongly suggests that it's not being grounded properly, which does require a working level unit.
At this point, set your multimeter to 2K ohms and test between the two center terminals of your pump module, which will be the level unit circuit. Expect to see something on this scale. If it remains an open circuit, you've simply got a bad level unit, which usually can be replaced separately but is probably best done with a whole pump unit if the pump has more than 80K miles on it. Pumps are iffy from that point and you'd benefit greatly from peace-of-mind from knowing that the pump will likely last for several more years if you replaced it now. Either way, it's gonna require pump unit removal.
By the way, the reason why your OBD system even cares about fuel level is for the Misfire Monitor and Evap Leak Monitor, both of which require a certain tank level before running their tests. It doesn't make sense to worry about misfire if the tank is dry, nor do they want the evaporative system tested when just-filled or too close to empty.