A B737-700 CREW WAS ERRONEOUSLY TOLD NO MEL WAS NEEDED WHEN THE CTR FUEL TANK PUMPS NEEDED PRIMING AND NOT FUNCTIONING.

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WE DEPARTED FOR ZZZ AND NOTICED FUEL IN THE CTR TANK. APPROX 500 LBS WHICH WAS EXTRA FUEL; NOT REQUIRED FOR THIS FLT. WE CLBED THROUGH 10000 FT AND I; PIC; ELECTED TO TURN 1 CTR PUMP ON AND OPEN THE XFEED VALVE. THE PUMP LOW PRESSURE LIGHT ILLUMINATED AND STAYED ILLUMINATED. I THEN TURNED THAT PARTICULAR PUMP OFF AND SELECTED THE OTHER PUMP ON. THAT LOW PRESSURE LIGHT REMAINED ILLUMINATED AS WELL. I THEN SELECTED BOTH PUMPS OFF AND CLOSED THE XFEED VALVE. I SENT A MAINT ACARS TO ZZZ TO HAVE MAINT MEET US IN THE FLT DECK AND TYPED; CHK CTR BOOST PUMPS. WHEN WE ARRIVED AT THE GATE MAINT WAS THERE TO GREET US. WE EXPLAINED THE PROB AND HE INFORMED US THAT THE PUMPS NEEDED TO BE PRIMED. TO PRIME THE PUMPS WE NEEDED TO ADD 14000 LBS OF FUEL. HE STATED THAT MAINT CTL AND BOEING WERE AWARE OF THIS PROB; AND WERE LOOKING INTO IT. I ASKED IF THIS NEEDED TO BE 'WRITTEN UP' AND HE STATED THAT IT DIDN'T. HE SAID THE NEXT TIME THEY NEEDED TO ADD FUEL TO THE CTR TANK THEY WOULD ADD THE APPROPRIATE AMOUNT AND IT WOULD BE ALRIGHT. WE LEFT IT AT THAT. APPROX 20 MINS LATER; THE FO AND I CAME TO THE CONCLUSION THAT THERE WOULD BE NO WAY OF ANOTHER CREW TO KNOW OF THIS PRIMING OF THE CTR BOOST PUMPS UNLESS THERE WAS SOMETHING IN THE RECORDS ALERTING THEM OR DISPATCH TO THIS. WE CALLED MAINT BACK TO THE JET. WHEN MAINT ARRIVED AND WE ASKED HIM THAT QUESTION; HE SAID THAT WAS A GOOD POINT AND CALLED MAINT CTL. HE CAME BACK A FEW MINS LATER AND SAID THAT IN ZZZ1 WE WOULD FILL THE CTR TANK TO 14000 LBS AND WOULD PRIME THE PUMPS. I ASKED AGAIN; 'DO WE NEED TO WRITE THIS IN THE LOGBOOK?' HE SAID NO AND MAINT CTL SAID NO AS WELL. WE CLOSED THE DOOR; COMPLETED THE CHKLIST AND TOOK OFF FOR ZZZ1. ON ARR IN ZZZ1 WE NOTICED THE FUEL LOAD ON THE RELEASE AND IT WASN'T SHOWING WE WERE TAKING OFF WITH CTR TANKS FULL; ASKED THE OPS AGENT IF HE KNEW ANYTHING ABOUT FULL TANKS AND PRIMING THE PUMPS AND HE SAID NO. I THEN CALLED DISPATCH AND ASKED THEM. HE SAID HE DIDN'T THINK THIS NEEDED TO BE WRITTEN UP AND GOT MAINT CTL ON THE PHONE. MAINT CTL GOT ON THE PHONE AND STATED THAT; 'YES; IT DID NEED TO BE WRITTEN UP AND MEL'ED. WE WROTE UP THE CTR BOOST PUMPS INOP IN THE LOGBOOK. MAINT IN ZZZ1 CAME TO THE JET TO DO THE MEL PROCS AND WE DEPARTED. I; AS PIC; SHOULD HAVE LISTENED TO MY INNER VOICE TELLING ME TO WRITE THIS UP. I SHOULD HAVE WRITTEN IT UP IN THE AIR WHEN I SENT THE ACARS TO ZZZ. MAINT AND MAINT CTL SHOULD HAVE ALL BEEN ON THE SAME PAGE WITH THE PLTS.