SMT BACK TAXIED DOWN ACTIVE RWY WITHOUT CLRNC FROM TWR; MISUNDERSTANDING BETWEEN FLT CREW AND GND CTLR.

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THE CAPT ACCEPTED TAXI FOR AN INTXN DEP FROM JULIET WITH THE UNDERSTANDING THAT BETTER THAN 7000' OF RWY REMAINED FOR TKOF ON RWY 12L. (WE WERE INFORMED THAT KILO WAS CLOSED.) THE CAPT INADVERTENTLY GOT OFF TXWY ALPHA ON INDIA WHICH I POINTED OUT TO THE CAPT. THE CAPT RESPONDED FOR ME TO REQUEST A BACKTAXI; WHICH HE AND I BOTH UNDERSTOOD TO MEAN ONTO THE RWY TO JULIETT; SO THE TKOF COULD BEGIN AT THE PROPER PLACE. I REQUESTED A BACKTAXI FROM GND CTL; WHO RESPONDED; 'THAT'S APPROVED;' OR 'BACKTAXI APPROVED.' THE CAPT AND I SCANNED FOR TFC ON FINAL APCH AND THERE WAS NONE. THE CAPT THEN TAXIED ONTO THE RWY TOWARD INTXN J. WE WERE THEN INFORMED BY GND THAT WE WERE NOT SUPPOSED TO BE ON THE RWY. THE CAPT THEN TOOK THE RADIO AND SAID THAT WE HAD UNDERSTOOD THAT OUR BACKTAXI DOWN THE RWY WAS APPROVED; AND THAT THE WAY WE HAD UNDERSTOOD OUR INSTRUCTIONS. (SINCE NO PERMISSION WOULD HAVE BEEN REQUIRED TO TURN AROUND ON INDIA AND TAKE ALPHA TO JULIET.) THE GND CTLR THEN INSTRUCTED US TO CONTINUE DOWN THE RWY AND EXIT AT JULIETT. I RPTED US CLR OF THE RWY AT J; AT WHICH TIME WE WERE INSTRUCTED TO CONTACT THE TWR FOR DEP. THE FLT DEPARTED W/O INCIDENT AND NO FURTHER REFERENCES WERE VERBALLY MADE RE: THE MISSED COMS OR RWY INCURSION. THIS SEEMS LIKE A CLASSIC CASE OF BEING IN TOO MUCH OF A HURRY TO COMMUNICATE COMPLETELY AND CONCISELY AND MAKING ASSUMPTIONS ABOUT WHAT SOMEONE ELSE HAS ASKED OR INSTRUCTED. CAPT SHOULD HAVE SAID: 'REQUEST A BACKTAXI DOWN THE RWY.' IF NOT; F/O SHOULD HAVE SAID TO THE CAPT: 'DOWN THE RWY?'; AND TO GND: 'DOWN THE RWY.' GND CTLR'S INSTRUCTIONS; 'BACKTAXI APPROVED;' SHOULD HAVE BEEN QUESTIONED. WHETHER OR NOT THE CREW USED THE TERM 'ON THE RWY;' OR; 'DOWN THE RWY;' THE GND CTLR SHOULD HAVE BEEN SPECIFIC IN HIS INSTRUCTIONS (WHICH HE IS TAUGHT AS PROC). EX: 'BACKTAXI IS APPROVED ON THE RWY; EXIT AT JULIETT AND CONTACT THE TWR.' OR; EX: 'BACKTAXI IS APPROVED; MAKE A LEFT 180 ONTO ALPHA TO JULIETT AND CONTACT THE TWR WHEN READY FOR DEP.'