CREW TAKES DSCNT CLRNC OF ANOTHER ACFT. CTLR MISSES THE READBACK AND TFC CONFLICT IS THE RESULT.

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I WAS FLYING AS CAPT; IN A CESSNA CITATION V. WE WERE AT FL350; ABOUT 86 NM SE OF PMM VOR ON A RTE THAT WOULD TAKE US TO PMM; THE BRAVE INTXN; AND FINALLY THE DEST OF RAC; WI. AT THAT TIME; ZAU STATED 'DSND TO FL240; EXPEDITE THROUGH FL290.' MY FO READ BACK 'DSNDING OUT OF FL350 FOR FL240; EXPEDITE THROUGH FL290.' WE HEARD NO FURTHER RESPONSE FROM ATC OR ANOTHER ACFT. I INITIATED A DSCNT AT 3000 FPM. MOMENTS LATER AN OBVIOUSLY EXCITED CTLR STATED; 'THAT DSCNT WASN'T FOR YOU; CLB IMMEDIATELY TO FL350; MAKE AN IMMEDIATE TURN TO 280 DEGS.' AS HE BEGAN THOSE STATEMENTS; WE RECEIVED A TCASII TA. MY RESPONSE WAS BRISK; STOPPING THE DSCNT; TURNING L; AND CLBING BACK TO FL350. WHILE DOING SO; THE SAME CTLR CAME BACK ON THE AIR; NOW APPEARING TO BE QUITE SHAKEN; DIRECTING HIS COMMENTS TO ANOTHER ACFT. HE SAID; 'N-YYYYY; THAT DSCNT WAS FOR YOU!' TO WHICH THE OTHER ACFT REPLIED; RATHER POINTEDLY; 'YOU NEVER GAVE US A DSCNT!' SHORTLY AFTER THAT; A DIFFERENT CTLR CALMLY STATED; 'ACFT X CLRED DIRECT PMM VOR.' I DID NOT GET THE TAIL NUMBER FROM THE OTHER ACFT. AND I CANNOT SAY IF THERE WERE 2 ACFT INVOLVED OR 3. I ASSUME 3; WITH MY ACFT BEING #1; ANOTHER ACFT AT FL350; FOR WHOM THE CLRNC WAS MEANT; BEING # 2; AND AN ACFT AT A LOWER ALT BEING #3.