FLT CREW TO ORF AT FL270 IS INSTRUCTED TO DSND BY ATC AND EXPERIENCED TCASII EVENT BECAUSE OF CTLR ACFT CALL SIGN IDENT ERROR.

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WHILE ADMINISTERING IOE FOR A CAPT CANDIDATE; ON INITIAL DSCNT FROM OUR CRUISING ALT OF FL270; WE EXPERIENCED AN NMAC WITH ANOTHER ACFT; ENRTE TO ORF FROM STL. A DSCNT CLRNC WAS ISSUED FROM FL270 TO FL260 BY ZDC. MY CAPT-IN-TRAINING; ACTING AS PNF; ACKNOWLEDGED 'DSND TO FLT LEVEL TWO-SIX-ZERO; ACR X.' I VERIFIED THIS ALT AND BEGAN MY DSCNT. AT APPROX FL265 OUR TCASII SYS ISSUED A TA FOR A CONFLICT AT FL260. THE COMMAND 'MONITOR VERT SPD' WAS ISSUED. AT THIS POINT; I DISCONNECTED THE AUTOPLT TO ARREST OUR DSCNT. ALSO; AT THIS MOMENT; ZDC ASKED US TO VERIFY WE WERE LEVEL AT FL270. AFTER THIS XMISSION; ATC ADVISED US TO TURN L; IMMEDIATELY; TO 360 DEGS (FROM OUR CURRENT HDG OF 115 DEGS). I ALSO ISSUED A 'CLB' COMMAND FROM OUR TCASII SIMULTANEOUSLY. AFTER COMPLYING WITH BOTH ATC AND THE TCASII TA/RA ADVISORY; I WAS LEFT AT APPROX FL280; ON A 030 DEG HDG. AT THIS POINT; OUR TCASII SYS ISSUED A 'CLR OF CONFLICT' AURAL ADVISORY. WE ATTEMPTED TO VERIFY WITH ZDC THAT WE WERE LEVEL AT FL280 AND ASK IF AT THE CURRENT TIME; THIS WAS AN ACCEPTABLE ALT. A SECOND ATTEMPT WAS MADE BY MY PNF TO VERIFY OUR NEW ALT OF FL280 WAS ACCEPTABLE WITH ZDC; TO WHICH WE RECEIVED NO RESPONSE. OUR NEXT INSTRUCTION FROM ZDC WAS A 'R TURN; CLRED DIRECT TO HARCUM (HCM) VOR; DSND AND MAINTAIN FL250.' AT THIS POINT I OUR FLT; MY PNF AND I DISCUSSED AND AGREED THAT ZDC HADE CLRED US TO DSND FROM FL270 TO FL260. THIS WAS READ BACK BY MY PNF; AND CONFIRMED (OR NOT CORRECTED OR CHALLENGED) BY OUR CTLR. BRIEFLY; OVER THE RADIO; I ASKED HIM WHAT HAD JUST HAPPENED. HE (ATC) RESPONDED WITH ANOTHER COMPANY FLT'S (NUMBER NOT GIVEN)DSCNT CLRNC. THIS POINT; I STRONGLY DISAGREE WITH. I ASKED FOR AND RECEIVED THE CTR'S PHONE NUMBER. AT THE COMPLETION OF OUR FLT; I CALLED AND SPOKE WITH THE ON-DUTY SUPVR. HE INDICATED THE SUPVR ON DUTY AT THE TIME OF OUR INCIDENT HAD LEFT AND THAT I COULD CALL BACK THE NEXT DAY BTWN THE HRS OF XA00 AND XH00. I GAVE HIM A BRIEF SUMMARY OF WHAT HAD HAPPENED; FROM OUR POINT OF VIEW. WHEN I ASKED HIM WHAT THE NEXT STEP WAS; HE INDICATED THAT THIS WAS 'INFO GATHERING ONLY.' I CALLED ZDC AND WAS ADVISED; AFTER SPEAKING WITH THE SUPVR; THAT A CTLR HAD MADE AN ERROR. HIS INTENTION WAS TO GIVE THAT CLRNC TO ANOTHER COMPANY FLT; AND HE MISTAKENLY HAD GIVEN US THE CLRNC TO DSND.