LOSS OF SEPARATION WHEN CTR CTLR AMENDED RPTR'S DC8 CLB ALT TO FL270 INSTEAD OF FL260.

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ZID HAD ASSIGNED US FL280 WHILE WE WERE CLBING TO A FINAL CRUISE ALT OF FL310. THIS ALT (FL280) WAS ASSIGNED SHORTLY AFTER INITIAL CONTACT WITH ZID. A FEW MINS LATER; ZID CHANGED OUR ASSIGNED ALT TO FL270. WE WERE IN THE MID TEENS AT THE TIME THIS ASSIGNMENT WAS MADE. OUR RATE OF CLB WAS APPROX 1000 FPM; SO 8-10 MINS ELAPSED BEFORE WE APCHED OUR ASSIGNED ALT OF FL270. AS WE PASSED THROUGH FL268 ATC CONTACTED US AND INFORMED US WE HAD BEEN ASSIGNED FL260. THE FO; AS PNF; TOLD ATC WE HAD BEEN ASSIGNED FL270. THE CTLR DENIED ASSIGNING US FL270. AS FP; WHILE THIS EXCHANGED OCCURRED; I DSNDED IMMEDIATELY TO FL260. LESS THAN 1 MIN AFTER LEVELING AT FL260; ATC CLRED US TO CLB TO FL310. WE REQUESTED A CONTACT PHONE NUMBER FROM ATC; AND UPON ARRIVAL AT PHX; I ATTEMPTED TO CONTACT ZID QUALITY ASSURANCE. THE SHIFT SUPVR INFORMED ME THAT THE MISTAKE HAD BEEN MADE BY THE CTLR; NOT US. THIS WAS BASED ON HIS REVIEW OF THE TAPES. MY CREW AND I FOLLOWED SOP REGARDING ATC COM AND CLRNC WHICH REQUIRES THE PF TO REPEAT THE CLRNC BACK TO THE PNF AFTER HE HAS ACKNOWLEDGED IT TO ATC. I PERSONALLY MAKE IT A PRACTICE TO BRIEF MY CREW THAT WE WILL ASK FOR CLARIFICATION OF ANY CLRNC IF ANY MEMBER OF THE CREW HAS DOUBTS ABOUT WHAT THE CLRNC WAS; OR DID NOT HEAR IT. I AM NOT SURE IF THERE WAS CONFLICTING TFC; AS WE DO NOT HAVE TCASII. I BELIEVE TCASII SHOULD BE REQUIRED ON ALL TRANSPORT CATEGORY ACFT. IF THERE WERE A CONFLICT IN THIS CASE TCASII MIGHT HAVE PREVENTED IT. THERE WAS A GREAT AMOUNT OF TFC ON FREQ AND I BELIEVE THE CTLR WAS SATURATED.