POTENTIAL CONFLICT WHEN A B737 FLT DSNDS TO THE SAME ALT AS OPPOSITE DIRECTION TFC AS THE CLRNC TO FL250 WAS QUESTIONED BY CTLR.

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I WENT BAC TO THE LAVATORY BEFORE WE BEGAN OUR DSCNT ON THE ORRY ARR. WE WERE AT FL370. WHEN I CAME BAC. THE CAPT BRIEFED ME ON ANY CHANGES WHICH WAS; CLRED TO FL250. AFTER SEVERAL MINS LATER; OUR TCASII GAVE A TA AND WE NOTICED TFC AT OUR 1 O'CLOC POS; OPPOSITE DIRECTION AT THE SAME ALT AND DID PASS OFF OUR R SIDE ABOUT 4 OR 5 MI. I THOUGHT THIS WAS STRANGE AND AS I WAS ABOUT TO QUESTION ZDC CTR ABOUT IT; THEY ASED US TO STATE OUR ALT; WHICH WE DID. THEY SAID WE LOST SEPARATION AND THAT WE SHOULD NOT BE AT THAT ALT BUT AT FL270 AND FOR US TO GIVE THEM A CALL. THE CAPT EXPLAINED THAT THE PREVIOUS CTLR CLRED US TO FL250 AND THAT WHEN HE CHED IN HE RESTATED OUR ALT; FL250. ABOUT 5 MINS LATER; ZDC TOLD US THAT EVERYTHING WAS O AND WE DID NOT HAVE TO CALL THEM. WE DO NOT NOW WHAT WE COULD DO DIFFERENT. MY QUESTIONS ARE; WHY DID IT TAE OVER 5 MINS BEFORE ATC QUESTIONED OUR ALT WHICH INVOLVED 2 DIFFERENT CTLRS? WHY DID NOT THEIR SYS PROJECT ANY CONFLICTS WHEN THEY CLRED US OR THE OTHER ACFT TO THAT ALT?