CAPT HEARD DSND FL310 AND READ BACK WHEN ARTCC CTLR WAS QUERIED; SHE CONFIRMED FL330.

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WHILE ON THE ARR TO DFW WE RECEIVED CLRNC TO DSND. I THOUGHT I HEARD 'CLRED TO DSND AND MAINTAIN 310.' I CLRLY AND DELIBERATELY RESPONDED 'ROGER; OUT OF 350 FOR 310.' THERE WAS NO RESPONSE FROM THE CTLR. I LOOKED OVER AT THE ALT SET WINDOW AND OBSERVED MY FO HAD SET 330. SHE LOOKED AT ME AND SAID SHE THOUGHT SHE HAD HEARD 330. TO VERIFY; I CALLED THE CTLR AND SAID; 'VERIFY XX CLRED TO 310.' SHE RESPONDED; 'NEGATIVE XX DSND TO AND MAINTAIN 330.' I THEN ASKED IF SHE HAD HEARD MY READBACK TO 310 AND SHE REPLIED; 'AFFIRMATIVE XX I UNDERSTOOD THAT.' I THEN ASKED; (AFTER DSNDING TO 330) WHY; IF SHE HEARD THE INCORRECT READBACK; SHE HAD NOT CORRECTED ME; TO WHICH SHE REPLIED; 'MAYBE IT DIDN'T SEEM CRITICAL.' IT WAS; OF COURSE; BEYOND BELIEF TO HEAR SUCH A RETORT. I ASKED HER FOR HER INITIALS AND A TELEPHONE NUMBER. SHE REPLIED; 'UNDER THE CIRCUMSTANCES I'M NOT GOING TO GIVE YOU MY INITIALS. YOU CAN CALL NUMBER.' THIS WHOLE INCIDENT POINTS TO A VERY DANGEROUS PERSONALITY PROBLEM. I'VE NEVER HEARD SUCH A CONVERSATION IN MY PROFESSIONAL CAREER. WHILE IT IS VERY IMPORTANT TO REALIZE THIS IS ONLY ONE CTLR AND ONE INCIDENT; IT CANNOT BE ALLOWED TO GO UNCHKED. THE ASSISTANT CHIEF OF THE ATC FACILITY WAS NOTIFIED RIGHT AWAY AND A PROMISE WAS MADE TO 'PULL THE TAPES' THE NEXT MORNING FOR A READOUT. AS OF THIS WRITING; I HAVE NOT HEARD FROM THE FACILITY.