POTENTIAL CONFLICT AS B727 PERFORMS A CLB THROUGH OCCUPIED ALT. CLRNC READBACK HEARBACK DISPUTED. OPERROR ADMITTED BY ATC. ARTCC RADAR CTLR EXPERIENCE LEVEL TECHNIQUE ATC COM.

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LOCATION: APPROX 80 NM W ALX; ON ZFW FREQ 126.57. ASSIGNED CLB TO FL330. REQUESTED DIRECT HARVEY VOR. TOLD TO REQUEST THAT ON NEXT FREQ. AT APPROX XA50Z; CHANGED TO ZFW 132.27. FO RPTED PASSING FL256 FOR FL330. ATC ACKNOWLEDGED. REQUESTED DIRECT HARVEY VOR. ATC CLRED US TO HARVEY. AT ABOUT XA54Z; ZFW CALLED TFC AT 12 - 1 O'CLOCK POS AT FL310. FO SAID LOOKING FOR TFC. I DECREASED RATE OF CLB AS I HAD AN UNEASY FEELING ABOUT THE SIT; IE; CLBING TO FL330 WITH TFC AT 12 O'CLOCK AT FL310. AS I PICKED TFC UP ON TCASII; WE GOT A TA WARNING AND FO GOT VISUAL AT 1 - 2 O'CLOCK POS; AT 8 NM. WE WERE NOW LEVEL AT FL300. ABOUT THAT TIME ZFW SAID WE WERE TO BE AT FL290; CONFIRM FL290. FO SAID WERE CLRED TO FL330. ZFW SAID DSND TO FL290. WE DID. NOBODY ON CREW EVER HEARD A CLRNC TO FL290. ATC SAID THEY WOULD CHK ON IT. BEFORE FREQ CHANGE WE ASKED ABOUT THE SIT. ATC SAID HE WAS A NEW CTLR AT THE PANEL AND TO FORGET ABOUT THE ALT PROB. WE THEN WENT TO ZHU. SUPPLEMENTAL INFO FROM ACN 356000: I ACQUIRED A B737 AT 1 - 2 O'CLOCK AND 8 MI. ATC SAID WE WERE SUPPOSED TO BE AT FL290; CONFIRM FL290. I SAID WE WERE CLRED BY LAST CTLR TO FL330. HE SAID NO; I CLRED YOU TO FL290; MAINTAIN FL290. SUPPLEMENTAL INFO FROM ACN 356107: THE FO SPOTTED THE TFC AT 1 - 2 O'CLOCK POS AND I ALSO SAW IT ABOUT 5-10 MI OFF. AT ABOUT THIS SAME TIME; ATC ASKED IF WE WERE LEVEL AT FL290. WE SAID NO; AND THAT WE WERE PASSING FL300. HE SAID 'I ASSIGNED YOU FL290 WHEN YOU CHKED ON.' THE FO SAID; 'NO; I THINK YOU FORGOT TO ASSIGN US FL290.'