To wrap up: I did make a second call to their customer support and was told the same lines as with the first one.
Now when I dropped the car (full) at the airport and presented a fuel receipt from a nearby gas station Dollar's receipt still listed the FPO. The receiving agent told me that I had to go to the information booth at the other end of the parking lot, and the agent there then, upon being presented the fuel receipt, deducted the FPO, not without pointing out though that they would not be obliged to do so. The final receipt did read USD 0.00, and to date, Dollar has not made an attempt to charge the credit card.
Making use of the FPO would have been almost $20 more expensive than filling up oneself.