B737 CREW WAS INSTRUCTED TO 'ROUND THE CORNER' WHILE APCHING RWY 16R IN RNO.

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AT XA02 WE PUSHED BACK FROM GATE X IN RENO AND SHORTLY BEGAN TAXIING TO RWY 16R. WE WERE FACING E AT THE APCH END OF RWY 16R MONITORING THE TWR FREQ. THE CLRNC WAS GIVEN 'TURN THE CORNER AND HOLD SHORT RWY 16R. AFTER RELEASING THE PARKING BRAKE AND READING BACK THE CLRNC; I HAD REALIZED THE HOLD SHORT RWY 16R COM ERROR BY THE CTLR. WE STOPPED SHORT OF RWY 16R; CLR OF THE RWY. THE LNDG LIGHTS WERE ON AT THE TIME AND PROVIDED US CLR VIEW THAT W WERE NOT ON RWY 16R. WE HEARD THE CALL FROM ANOTHER ACR Y JET GOING AROUND FOR THE SAME RWY. WE INFORMED THE TWR WE WERE NOT ON THE RWY AND HOLDING CLR OF RWY 16R. I NOTICED WHILE HOLDING SHORT OF RWY 16R THE LNDG/TAXI LIGHTS OF THE ACFT BEHIND US AT A 45 DEG POS (APPROX HDG OF 050 DEGS; A NE HDG) LATER TO BE IDENTED AS AN ACR ACFT. I CONTACTED THE RENO TWR ON ARR INTO LOS ANGELES AND WAS ASKED TO CONTACT MR X. WE HAD A BRIEF DISCUSSION OF WHAT HAD HAPPENED AT THE APCH END OF RWY 16R. MR X TOLD ME THAT 3 TWR CTLRS HAD VISUALLY ATTESTED THAT WE WERE NOT ON THE RWY 16R; BUT DUE THAT IT WAS NIGHT THERE MAY HAVE BEEN AN ERROR IN VIEWING. I ASSURED HIM THAT WE WERE NOT ON THE RWY OR THE DISPLACED THRESHOLD OF RWY 16R. IT WAS LATER IDENTED BY MR X AS THE ACR Z ACFT THAT HAD TOLD GND/TWR THAT WE WERE ON RWY 16R AND NOT HOLDING CLR OF THE RWY. I FEEL THAT THE RENO TWR CTLR HAD MISIDENTED OUR ACFT WITH THAT OF ACR Z WHO WAS FACING A NE HDG WITH LNDG/TAXI LIGHTS ON AT THE TIME TO ISSUE A TURN THE CORNER AND HOLD SHORT CLRNC. I'M NOT SURE IF THE CTLR HAD REALIZED THAT WE WERE HOLDING SHORT OR HAD MISIDENTED EITHER ACFT. WE HAD BEEN HOLDING SHORT OF RWY 16R SINCE XA09 FOR OUR SCHEDULED WHEELS UP (XA12) TIME FOR LOS ANGELES; AND WERE THE ONLY ACFT TAXIING OUT FOR DEP THAT WE WERE AWARE OF. AT THE TWR'S OPTION THEY COULD HAVE ASKED THAT WE HOLD OUR POS; AND SENT A VEHICLE TO THE APCH END OF THE RWY TO VERIFY OUR POS. A MORE APPROPRIATE CLRNC WOULD HAVE BEEN. HOLD SHORT RWY 16R. WITH OUR REPLY HOLDING SHORT RWY 16R. AS A NOTE; THIS RWY 16R HAD BEEN CLOSED FOR CONSTRUCTION DAYS PRIOR AND RECENTLY OPENED AGAIN. THE HOLD LINE IS NOT EASILY IDENTIFIABLE FOR THIS RWY. SUCH CLRNCS OF TURN THE CORNER AND HOLD SHORT ARE AN INVITATION FOR FUTURE ERRORS.