The meter is not lying. Very unlikely. Turn off the main valve at the house. See if the needle is still moving. You may have an underground leak somewhere.
3000 gallons in a month is about 100 gallons per day, about 4 gallons per hour. An underground leak, or a toilet fill valve running full blast, can easily acount for this. Check the overflow discharge pipe off the water heater. If it is pipes somewhere, see if the pipe is hot, and find the end to see if it is running.