FLC IS ALLEGED TO HAVE TURNED THE WRONG WAY TO GET TO A VECTOR HDG.

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MY COPLT WAS FLYING THIS LEG. WE WERE AT 8000 FT TRACKING THE LOC INBOUND TO RWY 36 AT DCA AND APPROX 15 MI OUT WHEN MY COPLT SAID TO ME WE COULD USE A LOWER ALT. I CALLED DCA APCH CTL AND ASKED FOR A LOWER ALT AND HE; DCA APCH CTL; CAME RIGHT BACK AND SAID 'YOU ARE CLRED FOR THE ILS TO RWY 36. CAN YOU MAKE IT DOWN OK OR WOULD YOU LIKE TO BE VECTORED FOR THE DSCNT?' I TOLD HIM WE WOULD LIKE TO BE VECTORED BACK OUT. HE SAID 'TURN TO A HDG OF 180 DEGS AND DSND TO 6000 FT.' I DO NOT REMEMBER HIM SAYING WHICH DIRECTION TO TURN AND I DO NOT REMEMBER SAYING WHICH WAY TO TURN IN MY READBACK OF THE CLRNC. MY COPLT STARTED AN IMMEDIATE TURN TO THE R AND A DSCNT TO 6000 FT. I ASSUMED THAT MY COPLT HAD HEARD THE APCH CTLR TELL US TO TURN TO THE R AND I DID NOT CLARIFY THE DIRECTION OF TURN WITH THE CTLR. SHORTLY AFTER WE STARTED OUR TURN TO THE R; THE CTLR TOLD US TO MAKE AN IMMEDIATE TURN TO THE L TO A HDG OF 270 DEGS BECAUSE THERE WAS TFC TO OUR R AT 6000 FT. WE DID MAKE AN IMMEDIATE TURN TO THE L AND THEN WE WERE VECTORED BACK OUT AND AROUND FOR THE ILS TO RWY 36 WITHOUT ANY MORE PROBS. I DO NOT BELIEVE THERE WAS ANY TFC CONFLICT AND WE NEVER RECEIVED ANY TCASII WARNINGS. WHEN MY COPLT STARTED THE TURN TO THE R; I SHOULD HAVE STOPPED HIM AND VERIFIED THE DIRECTION OF TURN WITH THE CTLR. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR FLIES AS CAPT FOR A MAJOR UNITED STATES ACR. THE RPTR AGREES THAT A R TURN TO S IS THE SHORT WAY AROUND AS THE ILS COURSE IS 005 DEGS. BUT THERE WAS A STRONG WIND FROM THE W WHICH WOULD HAVE MADE A L TURN SHORTER. THE RPTR BELIEVES THAT THE CTLR WAS BUSY AS HE FORGOT A DSCNT FOR THE RPTR. THERE WAS A LOT OF TFC AND FREQ CONGESTION. THE FACT THAT THERE WAS A LOW CEILING AND IT WAS NIGHT HELPED MAKE THE DECISION TO ASK FOR VECTORS FOR ANOTHER APCH. THE RPTR DOES NOT THINK THAT THE CTLR INDICATED WHICH WAY TO TURN. SUPPLEMENTAL INFO FROM ACN 296829: THE SURFACE WIND WAS 170 DEGS AT 10 KTS. THEY WERE LNDG DOWNWIND BECAUSE THE WX WAS BELOW MINIMUMS FOR THE LDA APCH TO RWY 18. THE TAILWIND AT ALT CONTRIBUTED TO MY BEING TOO HIGH CLOSE TO THE ARPT. I MISSED THE DIRECTION OF TURN AND TURNED R WHICH WAS THE SHORTER TURN TO HDG 180 DEGS.