A B737 FLT CREW IS TOLD BY THE GND CREW THAT THE ACFT IS CLR AND THAT ALL DOORS WERE CLOSED; WHEN IN FACT THEY WERE STILL RECEIVING FUEL.

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FLT WAS DISPATCHED TO TANKER FULL TO SF. THE FUELER WAS LATE STARTING FUELING AND IT LOOKED LIKE THE FLT WOULD BE DELAYED. THE AGENT ENTERED THE COCKPIT AND ASKED IF WE WERE READY AND WE TOLD HER WE NEEDED THE FUEL SLIP. SHE ACKNOWLEDGED AND THE FUELER WALKED UP RIGHT BEHIND HER AND HANDED US THE SLIP. WE SAID THAT WAS ALL WE NEEDED AND WE WERE READY. AS WE ENTERED THE FUEL TOTALS INTO ACARS; I NOTICED THAT THE TOTAL FUEL ON BOARD DID NOT MATCH; BUT IT WAS INCREASING. I ASSUMED THAT THE TOTALIZER WAS A LITTLE SLOW CATCHING UP; BUT THOUGHT THAT I HAD NEVER SEEN IT THIS SLOW BEFORE. NEXT; THE PUSHBACK CREW CALLED AND STATED WALK AROUND COMPLETE AND ALL DOORS AND PANELS CLOSED. I HAD THE FEELING THAT SOMETHING WASN'T RIGHT AND CHKED THE FUEL TOTALS AND THEY WERE STILL INCREASING RAPIDLY. I ASKED THE GND CREW IF THE FUELER WAS STILL HOOKED UP. HE WAS VERY APOLOGETIC AND ADMITTED THAT HE WAS. THE FO LOOKED OUT AND CONFIRMED THAT THE FUELER WAS STILL THERE AND SAID IT LOOKED LIKE HE WAS STILL FUELING! THAT'S WHEN WE REALIZED THAT WE WERE STILL RECEIVING FUEL WITH PAX ON BOARD AND ALL THE DOORS CLOSED. I COULDN'T SEE THE JETWAY DRIVER ANY LONGER AND JUST AS WE STARTED TO CALL TO OPEN THE DOOR AGAIN; THE FUELER FINISHED; UNHOOKED AND LEFT.