I agree that this is most likely an issue with the hydrometer or in reading it.
However, note that a 1.000 reading doesn't mean no sugars. As alcohol has a lower SG than water, high alcohol contents can cause lower than expected hydrometer readings. In fact, it's not unusual for a highly attenuated champagne to have a FG LOWER than 1. However, due to the unfermentabe sugars in malts, this is highly unlikely to happen to beer unless you get infected.