B-737 FLC MAKES APCH TO WRONG RWY.

Narrative

WE HAD AN FAA INSPECTOR IN THE JUMP SEAT GIVING US A LINE CHK. THERE WAS A LINE OF TSTMS JUST TO THE W OF THE FIELD MOVING PAST RAPIDLY. THE CEILING WAS 500 FT WITH VISIBILITY 7 MI IN RAIN. DURING DSCNT; WE BRIEFED THE APCH TO RWY 1L; BECAUSE WE WANTED THE LONG RWY DUE TO RAIN. WE WERE HANDED OFF TO APCH AND RECEIVED VECTORS TO THE ILS; WHICH WE ASSUMED WAS THE L. AT ABOUT 8-10 MI OUT; THE CTLR CLRED US FOR THE APCH. I RETURNED THE RADIO CALL AND SWITCHED TO TWR. I TOLD TWR WE WERE JOINING THE ILS TO RWY 1L. TWR SAID 'THE R OR L.' I SAID 'THE ILS RWY 1L APCH.' AT THIS TIME TWR SAID 'ROGER; CLRED TO LAND RWY 1L.' WE LANDED AND TAXIED TO THE GATE. AFTER ENG SHUTDOWN; THE FAA INSPECTOR ASKED IF WE WERE CLRED FOR THE ILS TO RWY 1L OR RWY 1R WHICH WE RESPONDED THE ILS TO RWY 1L. THE FAA INSPECTOR THEN CHKED THE TAPES AND WE WERE CLRED FOR THE ILS TO RWY 1R APCH. AT NO TIME DURING THE APCH DID THE FAA INSPECTOR QUESTION OUR APCH OR CLRNC UNTIL WE LANDED. AT NO TIME DID APCH OR TWR TELL US WE DID SOMETHING WRONG. DUE TO WX AND PREBRIEFING TO RWY 1L WE ASSUMED OUR CLRNC WAS TO THE L. A PROPER READBACK OF OUR APCH CLRNC WOULD HAVE SOLVED THE PROB WITH APCH INSTEAD OF WAITING TO CLARIFY WITH TWR. ALTHOUGH WE WERE EVENTUALLY CLRED FOR THE L AND IF WE WOULD HAVE HEARD HIM CLR US TO THE R; WE WOULD HAVE ASKED FOR THE L; WE STILL DID NOT THINK A VIOLATION WAS FORTHCOMING.