POTENTIAL CONFLICT BETWEEN 2 ACR ACFT IN IMC CONDITIONS. PLT DEVIATION OR OPERATIONAL DEVIATION.

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DEPARTED DCA AND WAS CLRED TO CLB AND MAINTAIN 9000'. AT APPROX 8700' CLBING; WASH APCH CTLR ADVISED US TO 'TURN HARD RIGHT AND DSND IMMEDIATELY TO 8000'.' WE HA TO MAKE WHAT WE THOUGHT WAS AN EVASIVE MANEUVER TO PREVENT A COLLISION; AS WE WERE IMC IN THE CLOUDS. AFTER LNDG AT EWR; I CALLED THE CTLR ON THE TELEPHONE AND WAS ADVISED THAT HE HAD ANOTHER ACFT; ACR Y; WHICH HAD JUST DEPARTED DULLES ARPT AND WAS AT 9000' INSTEAD OF HIS ASSIGNED 10000'. THE CTLR SAID HE HAD NO CONTACT WITH ACR Y; SO HE GAVE ME THE AVOIDANCE MANEUVER. IT SOUNDS AS IF ACR Y WAS AT THE WRONG ALT (9000' VERSUS 10000') OR ATC HAD ASSIGNED HIM A WRONG ALT. ONE OF MY PAX COMPLAINED TO THE NEWS MEDIA OF AN ABRUPT MANEUVER. I DON'T FEEL IT WAS THAT ABRUPT AND ALL OTHER PAX THANKED US FOR ADVISING THEM OF WHAT HAD TAKEN PLACE (OVER THE PAX ANNOUNCEMENT SYS DURING FLT; SHORTLY AFTER THE EVASIVE MANEUVER). CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: FROM DEST THE RPTR CALLED BACK TO DCA TRACON AND TALKED TO SUPVR. ATC SAID THAT NORMALLY THOSE IAD DEPS CLB TO 10000' AND THEN ARE CHANGED TO DCA FREQ. DCA CTLR SAW ACR Y MODE C LEVEL AT 9000'; SO GAVE TURN TO RPTR; ACR X; WHEN THE ACFT WERE STILL ABOUT 8 MI APART. CTLR THEN THOUGHT 3 MI LAT MIGHT BE LOST; SO TOLD X TO MAKE 'HARD RIGHT TURN' AND DSND TO 8000'. SUPVR ADVISED RPTR THAT LAT SEP DID NOT GET ANY LESS THAN 5 MI DURING AVOIDANCE MANEUVER. CTLR ANXIETY IN VOICE AND FACT THAT THEY WERE IN IMC MADE THE INCIDENT VERY FRIGHTENING. HAS HEARD NO FURTHER WORD SINCE CALL TO SUPVR.