DC9 FLT CREW RPTS AN NMAC WITH A B737 ON APCH TO PARALLEL RWYS AT BNA.

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APPROX 12 MI N OF BNA AT 2500 FT MSL; WE TOLD ATC THAT WE HAD THE ARPT IN SIGHT. ATC TOLD US THAT TFC FOR OUR RWY WAS A FLT OF 2 C130'S. WE WERE ABLE TO SEE THE 2 C130'S FROM OUR POS AND CALLED THE ACFT AND THE ARPT IN SIGHT. ATC THEN CLRED US FOR THE VISUAL APCH TO BNA RWY 20R. I DISCONNECTED THE AUTOPLT AND HAND FLEW THE ACFT FOR THE REST OF THE APCH AND LNDG. THE APCH CTLR TOLD US THAT TFC WOULD BE XING OVER THE TOP OF US FOR RWY 20L. HE THEN CLRED US DOWN TO 2000 FT MSL. THE TWR CTLR CALLED OUT THE TFC THAT WOULD BE XING OVER THE TOP OF US FOR RWY 20. WE SPOTTED THE ACFT AT 2 O'CLOCK AND ABOUT 5 MI VISUALLY AFTER SEEING THE ACFT'S LOCATION ON TCAS. I WAS SURPRISED TO SEE THE ACFT THAT WAS SUPPOSED TO FLY OVER THE TOP OF US SO CLOSE TO THE ARPT. THE TWR CTLR HAD ALSO MENTIONED THAT THE ACFT WAS ACR XXX B737. GIVEN ACR XXX'S PLT'S HABIT OF FLYING SHORT APCHS AND TAXIING FAST; I WASN'T AS SURPRISED THAT THEY WOULD BE DOING SOMETHING LIKE THIS SHORT APCH THEY WERE ABOUT TO UNDERTAKE AS IF THE ACFT HAD BEEN FROM ANY OTHER ACR. I HAVE NEVER WITNESSED ANOTHER ACR ACFT ATTEMPT TO DO WHAT ACR XXX WAS ABOUT TO TRY TO DO. WHILE CONTINUING TO MONITOR THE ACFT VISUALLY AND ON TCAS; WE RECEIVED A TFC ALERT. GIVEN THE TRAJECTORY THAT I WAS ESTIMATING AND OUR CLOSURE RATE; I DETERMINED THAT THE ACFT WOULD INTRUDE ON OUR FINAL APCH PATH. I TOLD THE PNF THAT THIS WAS NOT GOING TO WORK AND THE PNF QUERIED THE TWR CTLR TO VERIFY THAT THE ACR B737 CREW HAD US IN SIGHT. ATC CONFIRMED WITH THE B737 CREW OUR POS AND TO VERIFY THAT THEY HAD US IN SIGHT. THEY CONFIRMED THAT THEY DID HAVE US IN SIGHT. I STARTED TO DSND OUT OF 2000 FT MSL AND WE RECEIVED A TCAS RA INDICATING THAT WE SHOULD DSND. THE B737 WAS NOW XING DIRECTLY IN FRONT OF US FROM R TO L AND SLIGHTLY ABOVE OUR FLT PATH. THE TCAS INDICATED THE INTRUDER WAS +300 AT THE CLOSEST POINT. THE B737 OFFERED TO EXECUTE A 360 DEG TURN TO THE TWR CTLR BEFORE LNDG ON RWY 20L. THE TWR CTLR STATED THAT THE 360 DEG TURN WAS NOT NECESSARY AND THAT THEY WERE CLRED TO LAND. ATC AGAIN ASKED THE B737 CREW IF THEY HAD HAD THE TFC IN SIGHT. THE B737 PLT STATED THAT THEY HAD HAD THE TFC IN SIGHT; BUT THAT THEY HAD THE WRONG TFC IN SIGHT. THE REMAINDER OF OUR APCH AND LNDG WAS UNEVENTFUL. A B737 PROCEEDED TO RWY 20L AND LANDED. I ALSO HAVE TO ADD THAT I WAS THE PF; I WAS HAND FLYING THE ACFT (THE AUTOPLT WAS DISCONNECTED); I HAD THE INTRUDER ACFT IN SIGHT; AND THAT THERE WAS NO CHANCE THAT I WAS GOING TO LET OUR ACFT COLLIDE. I WAS IN POSITIVE CTL OF OUR ACFT AT ALL TIMES. PREVENTIVE MEASURES: XXX AIRLINES NEEDS TO SLOW DOWN; IN THE AIR AND ESPECIALLY ON THE GND. ATC SHOULD NOT ALLOW A MANEUVER SUCH AS THE ONE ATTEMPTED HERE. JETS XING OVER THE TOP OF ONE ANOTHER IN CLOSE PROX TO LNDG ISN'T SAFE AND DOESN'T PROMOTE SAFE FLYING. I NEED TO MAINTAIN A MORE CRITICAL POINT OF VIEW IN MY ANTICIPATION OF WHAT OTHER ACFT MAY OR MAY NOT DO. I LET MYSELF BELIEVE WHAT THE CTLR SAID WOULD BE TRUE. AS THE SITUATION PLAYED OUT; I HAD TO CONVINCE MYSELF THAT IT WASN'T EXECUTING THE WAY IT WAS SUPPOSED TO. ATC ISSUED A CLRNC FOR AN ACFT TO FLY OVER ANOTHER ACFT ON FINAL APCH AND THEN FAILED TO ADEQUATELY MONITOR THE 2 ACFT. OTHER THREATS NOT LISTED ABOVE THAT CONTRIBUTED TO THE EVENT: ATC ISSUED A CLRNC FOR THE B737 TO FLY OVER THE TOP OF OUR ACFT TO LAND ON THE RWY THAT IS CLOSE TO THE ACR GATES. HAVING TO MONITOR AN ACFT THAT WAS SUPPOSED TO FLY OVER THE TOP OF US; BUT INSTEAD FLEW ACROSS AND SLIGHTLY ABOVE OUR FLT PATH WITH APPROX 300 FT OF SEPARATION BTWN OUR ACFT WAS AN UNNECESSARY DISTR. WE WERE FORCED TO MONITOR THE OTHER ACFT WHEN WE SHOULD HAVE BEEN FOCUSED ON THE FINAL APCH AND LNDG.