A B727 FLT CREW HAVE AN ALTDEV DUE TO MISUNDERSTANDING THE ASSIGNED ALT BY ZDV.

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WHILE ENRTE DIRECT FROM TOLEDO TO DENVER; LEVEL AT FL260 APPROX 77 MI FROM DENVER; WE RECEIVED A CLRNC FOR DSCNT FROM FL260 AT PLT'S DISCRETION TO AND I BELIEVED AT THE TIME TO FL200. MY FO WAS PERFORMING RADIO COMS ON THE LEG FROM TOLEDO TO DENVER. THE FLT DECK CREW SET FL200 IN THE FLT ALT ALERTER AND ACKNOWLEDGED THE SETTING PER THE PROCS. AT 55 MI FROM THE ARPT GND SPD 380 KTS; I BEGAN MY DSCNT TO FL200 AND INFORMED THE FO TO CALL US OUT OF FL260 DSNDING TO FL200. THE FO AND MYSELF BELIEVE THIS WAS ACCOMPLISHED AND ZDV ACKNOWLEDGED THE CALL. I OBSERVED TFC IN THE 11 O'CLOCK POS. THE TFC REMAINED VISIBLE DURING THE DSCNT WITHOUT CONFLICT. AFTER PASSING FL220 ZDV QUESTIONED ASSIGNED ALT RADIO XMISSIONS BTWN THE FO AND ZDV IMPLIED HE WANTED US AT FL220 SO AT FL208; I INITIATED AN IMMEDIATE CLB TO FL220. SHORTLY AFTER THIS WE WERE CLRED TO FL200. WE THEN REVERSED THE ASCENT NEAR FL220 BACK TO FL200. THE 11 O'CLOCK POS TFC REMAINED IN SIGHT; EVEN DURING THE RETURN TO FL220 AND DSCNT TO FL200 I FELT THE VISUAL SEPARATION REMAINED SAFE. AS A FLT DECK CREW MEMBER AT NO TIME DID I QUESTION OR REALIZE THAT OUR ASSIGNED ALT WAS OTHER THAN FL200. AND ONCE PLACED INTO THE ALT ALERTER ALL CREW MEMBERS WOULD RECOGNIZE THAT AS THE ASSIGNED ALT AND USE THAT SETTING AS A REF. SUPPLEMENTAL INFO FROM ACN 599931: COCKPIT CREW BELIEVED CLRNC WAS TO FL200 ALTHOUGH DENVER VIA TELEPHONE ADVISED TAPES INDICATE FL220 WAS ACKNOWLEDGED.