ACR DESCENDED THROUGH ANOTHER FLT'S ALTITUDE AFTER RECEIVING DESCENT CLRNC.

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THIS OCCURRED SOMEWHERE N OF HOUTN INTXN ALONG OUR FILED RTE TO IAD. WHILE IN THE DSCNT FROM FL280 TO FL200 WE WERE ADVISED OF A WBOUND ACFT AT OUR 9 O'CLOCK POS. I ADVISED ATC THAT WE WERE LOOKING FOR TFC. THE OTHER PLT LET ATC KNOW THAT THEY HAD US IN SIGHT AND SHORTLY AFTER THAT; WE ACQUIRED VISUAL CONTACT WITH THEIR ACFT. AS WE WERE DSNDING THROUGH FL245; THE OTHER PLT CAME OVER THE RADIO ASKING CTR WHAT THE OTHER ACFT (US) WAS DOING. IN THE MEANTIME; THE CAPT AND I HAD NOTICED THE OTHER ACFT GETTING UNUSUALLY CLOSE AND HAD BEEN MONITORING ITS PROGRESS ON TCAS. AT THIS POINT; WE HAD ALREADY INCREASED OUR RATE OF DSCNT TO ENSURE SUFFICIENT CLRNC WITH THE OTHER FLT. VERY SHORTLY AFTER THIS THE ZNY CTLR CAME OVER THE RADIO DEMANDING TO KNOW OUR ASSIGNED ALT. THE CAPT TOOK THE RADIOS AT THIS TIME AND INFORMED THEM THAT WE WERE CLRED TO FL200. WE WERE THEN TOLD BY ATC THAT NO; WE WERE SUPPOSED TO HAVE STOPPED AT FL250. THIS CORRECTION WAS NOW BEING POINTED OUT BY A NEW VOICE; DIFFERENT FROM THE OTHER VOICE THAT ORIGINALLY CLRED US DOWN TO FL200. AT NO TIME WAS THERE ANY INSTRUCTION OR READBACK ON OUR BEHALF FOR US TO LEVEL AT FL250 AND ALSO; NO TA/RA OCCURRED AND VISUAL SEPARATION WAS MAINTAINED AT ALL TIMES. AFTER BEING ADVISED OF THIS BY THE NEW CTLR; WE ASKED SEVERAL TIMES FOR CLARIFICATION WITH NO RESPONSE AND WERE EVENTUALLY TOLD TO CONTINUE TO FL200. WE CONTINUED OUR FLT WITHOUT ANY FURTHER INCIDENT.