F100 FLC CHALLENGED BY MMLO APCH FOR NOT FLYING THE CLRED APCH.

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ON THE ARR; (V-39) TO MMLO LEON MEXICO; LEON APCH CLRED US TO FLY THE 'VOR/DME 2 RWY 31; RPT INTERCEPTING THE 12 DME ARC.' THE VOR DME 2 RWY 13 WAS IN THE FMS AND WE WERE SURPRISED TO HEAR THAT LEON HAD SWITCHED TO RWY 31 (AREA WX INDICATED 13). I; THE FO; QUERIED THE CTLR A SECOND TIME AS TO THE APCH TO BE FLOWN AND THE RESPONSE WAS 'VOR/DME 2 RWY 31.' THE CAPT AND I BOTH HEARD THE SAME RESPONSE AND BEGAN TO SET UP THE FMC/EFIS FOR THE NEW APCH. THE CAPT ELECTED TO REMAIN AT MINIMUM SECTOR ALT AND REF RAW DATA TO EXECUTE THIS APCH CLRNC FROM OUR PRESENT POS. I BRIEFED THE APCH AS THE CAPT BEGAN AN INTERCEPT HEADING FOR THE 12 DME ARC FOR RWY 31. APPROX 4 MINS INTO THE MANEUVER; LEON APCH ASKED US IF WE HAD INTERCEPTED THE 12 DME ARC. I REPLIED; 'WE ARE IN THE PROCESS OF INTERCEPTING THE 12 DME ARC.' THE CTLR THEN CLRED US TO COMMENCE THE APCH. APPROX 2 MINS LATER; THE CTLR ADVISED US THAT 'MEXICO CITY CTR HAD US ON RADAR N AND E OF THE 12 DME ARC.' MY REPLY WAS 'THAT'S CORRECT' BASED ON OUR GEOMETRY COMING FROM V-39 TO THE VOR/DME 2 RWY 31. THE CTLR THEN SAID WE WERE OUT OF POS FOR RWY 13 AND TO PROCEED DIRECT TO THE BJX VOR AT 11000 FT. THE CAPT ELECTED NOT TO DSND BELOW GRID MORA; 12000 FT; UNTIL ESTABLISHED ON SOME SEGMENT OF SOME APCH THAT THE CTLR AND US AGREED ON. IT WAS AT THAT POINT THAT I QUERIED THE CTLR AS TO WHICH APCH HE WOULD LIKE US TO FLY. HE SAID UPON REACHING THE VOR; YOU ARE CLRED TO FLY THE VOR/DME 1 RWY 13; RPT FINAL. THIS WAS THE FIRST TIME WE HAD HEARD RWY 13. WE COMMENCED THE VOR/DME 1; RWY 13 UNEVENTFULLY AND LANDED. ON THE GND; THE CTLR SAID EMPHATICALLY THAT HE CHKED THE TAPES; AND THAT HIS ORIGINAL CLRNC WAS TO FLY THE VOR/DME 2 RWY 13. NEITHER THE CAPT NOR I EVER HEARD THIS CLRNC; RATHER WE BOTH HEARD THE CLRNC TO RWY 31. THIS IN OF ITSELF IS A HUGE ISSUE; BUT IN MEXICO WITH THE LANGUAGE BARRIER AND TERRAIN IT HAD ALL THE MAKINGS OF CALI.