AN ACR'S ATC CLRNC RESULTED IN LESS THAN APPLICABLE SEPARATION MINIMA. THE CAPT QUERIED; AND DSNDED TO LOWER ALT; FOLLOWING ATC'S DIRECTION.

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IN CRUISE/CLB PHASE OF FLT; ZID HAD CLRED US (XXX) TO FL250. I ACKNOWLEDGED THE CLRNC. THE FO; WHO WAS FLYING THE LEG SET THE ALT (FL250) INTO THE AUTOPLT/ALT ALERTER AND ACTIVATED THE AUTOPLT TO CLB TO FL250. I REPEATED THE ALT 'FL250' WHEN I HAD SEEN THE ALT ALERTER SET CORRECTLY. SEVERAL MINS PASSED. SHORTLY; I NOTICED ANOTHER ACFT AT WHAT APPEARED TO BE OUR SAME ALT AND NOT MORE THAN 4 MI AWAY. THE OTHER ACFT; A BOEING 727 WAS RECOGNIZABLE FROM OUR COCKPIT. HE WAS GOING OUR SAME; OR NEARLY SAME; DIRECTION. TCASII DISPLAY ON OUR ACFT CONFIRMED WE WERE AT THE SAME ALT. I THEN ASKED ZID; 'ZID; XXX; DO YOU HAVE TFC FOR US AT 11 O'CLOCK?' CTR; 'XXX; CONFIRM YOU ARE LEVEL AT FL240.' I REPLIED; 'NEGATIVE; WE WERE CLRED TO FL250 AND WE ARE LEVEL AT FL250.' CTR; 'DSND AND MAINTAIN FL240.' I REPLIED; 'LEAVING FL250 FOR FL240; XXX.' ONCE WE WERE LEVEL AT FL240; THE FO AND I AGREED THAT ANOTHER RADIO XMISSION WAS NECESSARY. I XMITTED; 'ZID; XXX; WILL THERE BE A RPT FILED REGARDING THIS INCIDENT?' CTR REPLIED; 'YES.' THE FO AND I DISCUSSED THE INCIDENT AND WONDERED WHY CTR HAD MADE THIS MISTAKE AND HAD NOT ADVISED US OF THE OTHER ACFT. WE QUESTIONED WHY SEPARATION HAD BEEN LOST AND WHY HAD THE ALARM NOT SOUNDED AT ZID. WE WERE BOTH CERTAIN WE HAD BEEN CLRED TO FL250. WE DISCUSSED MAKING SOME NOTES OF WHAT HAPPENED FOR OUR RPT. WE ALSO AGREED THAT WE SHOULD MAKE AN ATTEMPT TO RETAIN OUR RECORDING OF WHAT TRANSPIRED. IT WAS APPARENT TO BOTH OF US THAT ZID WAS OPERATING AT A DEGRADED STATE FOR THE REASONS PREVIOUSLY DISCUSSED -- NOT PROVIDING SEPARATION; NOT ADVISING ACFT OF OTHER TFC THAT IS CLOSE; AND NOT HAVING AN OPERATING WARNING SIGNAL AT THE CTR WHEN SEPARATION IS LOST. THE FO AND I BOTH AGREED THAT WE SHOULD PULL THE CIRCUIT BREAKER FOR THE COCKPIT VOICE RECORDER TO RETAIN THE RECORDING OF WHAT HAD HAPPENED. THE FLT CONTINUED ON TO DEST WITHOUT INCIDENT. AT THE DEST POINT; I THEN PHONED OUR FLT OPS; DISPATCH; AND CHIEF PLT TO RPT WHAT HAPPENED. I WAS THEN DIRECTED TO UTILIZE AN UNMANNED STATION AIRWORTHINESS RELEASE TO DISPATCH THE AIRPLANE TO THE NEXT DEST WHERE THE COCKPIT VOICE RECORDER COULD BE REPLACED. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR CITED CONCERNS ABOUT ATC'S CONFLICT WARNING SYS. HE ALSO STATED THAT HIS COMPANY'S SAFETY COMMITTEE WAS TOLD THAT THE TAPE RECORDERS WERE DOWN DURING THE INCIDENT. THIS LEAVES THE COCKPIT VOICE RECORDER TAPE AS THE ONLY VERIFICATION OF WHAT HAPPENED. COCKPIT VOICE RECORDER VERIFIES FL250 CLRNC. THE CAPT'S PRIMARY CONCERN IS SAFETY. HE WONDERS WHAT FOLLOW-UP WAS ACCOMPLISHED; SINCE THE INCIDENT WAS NOT RECORDED; BUT DOES NOT WANT TO BE PUBLICLY ACCUSED OF UNLAWFUL TAMPERING (COCKPIT VOICE RECORDER CIRCUIT BREAKER PULLED TO STORE EVENT RECORDING; AND THEN MEL'ED). RPTR WAS UNCERTAIN AS TO WHETHER THIS ISSUE WAS EVER ADDRESSED BY ATC. ANALYST STATED THAT THIS TYPE OF INCIDENT WOULD NORMALLY LEAD TO RECERTIFICATION AND TRAINING REVIEW. SUPPLEMENTAL INFO FROM ACN 304960: ACR PROCS ON ALTS: 1 PLT RPTS LEAVING 1 FOR THE OTHER AND SETS IT IN THE ALT REMINDER WINDOW WHILE THE OTHER PLT CONFIRMS THE PROPER ALT IS SET. I AM CERTAIN WE WERE AT THE ASSIGNED ALT (FL250) AND THAT WE COMPLIED WITH THIS PROC. WE CHKED THE MEL AND FOUND REF SHOWING THE ITEM TO BE INOP.