ACR FLC HAD BEEN CLRED FOR A VISUAL APCH AFTER QUESTIONING THE CTLR ABOUT TFC AT THEIR 12 O'CLOCK POS. THE TFC HAD BEEN OBSERVED ON THE TCASII AND NOT VISUALLY. WHILE ON THE APCH; THE FO INQUIRED ABOUT AND RECEIVED THE POS OF THE TFC. THE TWR SUPVR CAME ON THE FREQ AND ARGUED WITH THE FO WELL INSIDE THE OM ABOUT WHY THEY DIDN'T HAVE THE TFC IN SIGHT.

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WE WERE CLRED FOR THE VISUAL ON RWY 5 AFTER WE ADVISED WE HAD THE RWY IN SIGHT. BEFORE THIS; SHE HAD ADVISED US TO A HDG TO INTERCEPT THE ILS RWY 5. WE NOTICED 1 ACFT IN FRONT OF US ALIGNED WITH THE RWY. THE TCASII GAVE US (AFTER WE WERE ESTABLISHED ON THE LOC) AN ACFT APCHING L TO R ON A 90 DEG ANGLE WITH OUR FLT PATH AT OUR ALT. MY FO (PNF) REQUESTED IF APCH WAS WORKING THE TFC 12 O'CLOCK. APCH ANSWERED 'AFFIRMATIVE; YOU ARE CLRED FOR THE VISUAL.' AT ABOUT 6 MI WE INQUIRED ABOUT THE TFC. APCH ADVISED US OF HIS POS AND STATED; 'I THOUGHT YOU HAD THE TFC IN SIGHT?' WE ADVISED WE DID NOT. AT THIS TIME; THE SUPVR CAME ON AND QUESTIONED US WHY WE DID NOT HAVE THE TFC. MY FO ADVISED HIM THAT WE NOTICED THE TFC ON TCASII; NOT VISUALLY. THE SUPVR STARTED TO ARGUE ABOUT WHETHER OR NOT WE HAD THE TFC AND THAT HE 'ASSUMED' WE HAD THE TFC IN SIGHT. THIS CONTINUED UNTIL WELL INSIDE THE OM; UP TO AN ALT OF 1129 FT AGL (I NOTICED THE RADAR ALTIMETER); WHEN MY FO REQUESTED TO SWITCH TO THE TWR. AT ONE TIME; I ADVISED THE SUPVR THAT WE NEVER MADE THE STATEMENT OF TFC IN SIGHT. WE CONTINUED THE APCH WITHOUT ANY CONFLICT WITH A SUCCESSFUL LNDG. ON THE GND I CALLED THE SUPVR AND STATED MY CONCERN NOT SO MUCH ABOUT THE MISUNDERSTANDING BUT THAT THE SUPVR CONTINUED TO QUESTION US WELL INSIDE THE OM IN THE MOST CRITICAL PHASE OF THE FLT.