CESSNA 150 INSTRUCTOR; WITH STUDENT; TAXIED ONTO ACTIVE RWY BELIEVING THAT THEY WERE FOLLOWING THEIR TAXI CLRNC TO BACK TAXI ON THE RWY; AND THEN OBSERVING AN ACFT ON FINAL. INSTRUCTOR TOOK ACFT CTLS TO EXIT THE RWY WHILE THE TWR SENT THE OTHER ACFT AROUND.

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RETURNING TO THE ACFT; THE STUDENT CALLED CLRNC DELIVERY; GOT HIS SQUAWK AND DEPARTURE CTL FREQUENCY; WHICH HE READ BACK CORRECTLY. WE TAXIED TO THE EDGE OF THE FBO RAMP; AND IN CONJUNCTION WITH THE ATIS INSTRUCTION; CALLED TWR FOR TAXI. I HAD THE STUDENT REQUEST 'INTERSECTION JULIET DEP.' THE STUDENT AND I BOTH HEARD 'BACK TAXI RWY ONE-SEVEN L TO INTERSECTION JULIET.' THE STUDENT READ THIS INSTRUCTION BACK. I THOUGHT IT WAS UNUSUAL THAT WE WOULD BE TAXIING ON THE RWY; BUT JUST THEN A BUSINESS JET EXITED THE RWY AT TXWY LIMA AND PROCEEDED N ON TXWY BRAVO. I CONCLUDED THAT THE CTLR WAS KEEPING US OUT OF THE JET'S BLAST. JUST PRIOR TO ENTERING RWY ONE-SEVEN L (AT LIMA); I HAD THE URGE TO CONTACT TWR AND VERIFY THE TAXI INSTRUCTION; BUT FAILED TO ACT ON THIS URGE. THE ONLY REASON I DIDN'T WAS BECAUSE THE STUDENT AND I WERE BOTH SURE OF WHAT WE HEARD. AS WE ENTERED ONE-SEVEN L; WE OBSERVED AN ACFT ON FINAL (ABOUT A MILE OUT; I WOULD GUESS) FOR THE RWY. I TOOK CTL OF THE ACFT AND STARTED A ONE-EIGHTY JUST AS THE TWR CTLR SAID '(A/C ID) YOU ARE ENTERING THE RWY' FOLLOWED BY A GAR INSTRUCTION TO THE ACFT ON FINAL. AFTER WE WERE OFF THE RWY; I EXPLAINED THAT WE WERE FOLLOWING OUR TAXI CLRNC. THE TWR OPERATOR DENIED ISSUING THAT CLRNC; BUT WAS CORDIAL AND SAID 'IT TURNED OUT ALL RIGHT; NO HARM DONE.' I ALMOST WISH WE HAD PULLED THE TAPES; BECAUSE I AM FAIRLY POSITIVE IN WHAT I HEARD; AND THE STUDENT CONCURS -- IN FACT; HE HAD INDEPENDENTLY READ BACK THE SAME INSTRUCTION. THE REASONS I DID NOT ASK FOR THE TAPES TO BE PULLED WERE; IN THE FIRST PLACE; I HAD NO WISH FOR THE TWR CTLR TO BE 'IN TROUBLE;' AND IN THE SECOND PLACE; ON THE OFF CHANCE THAT BOTH MY STUDENT AND I MIS-HEARD THE CLRNC; I THOUGHT THAT ASKING FOR THE TAPES TO BE PULLED MIGHT BE SEEN AS A 'NON-COOPERATING ATTITUDE;' AND MY EXPOSURE TO SANCTION MIGHT BE GREATER. IN THE FUTURE; I WILL POSITIVELY QUESTION ANY CLRNC OUT OF THE ORDINARY.