A B737 FLT CREW RECEIVE A TCASII RA AND DSND TO AVOID A LEARJET.

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TFC COMING DIRECTLY AT US FROM 1 O'CLOCK POS AND DSNDING; LEARJET (800 FT ABOVE US) CAUSED A TA. HIGH RATE OF CLOSURE CAUSED ALMOST IMMEDIATE RA OF 'DSND.' WE DSNDED BY 500 FT TO FL255. THE PLANE CLBED. MINIMUM VERT SEPARATION WAS 400 FT AT APPROX 3 MI; BUT A LITTLE MORE THAN THAT (NOT SURE HOW MUCH) WHEN TFC PASSED DIRECTLY OVERHEAD. UPON ARR AT ATL; I TELEPHONED ZDC. THE SUPVR SAID IT WAS 'CTLR ERROR.' THANK GOD FOR TCASII; AND ALSO THAT PLTS RESPONDED TO THEIR RA. RECOGNIZING HIS ZDC CTLR HAD TOLD HIM TO 'EXPEDITE DSCNT;' ACFT Y REFUSED; INSTEAD INFORMING CTLR THEY WERE CLBING TO COMPLY WITH TCASII RA. HAD THEY LISTENED TO ATC; RATHER THAN THEIR RA; A FATAL ACCIDENT MIGHT VERY WELL HAVE OCCURRED; AND WOULD HAVE CLAIMED THE LIVES OF 130+ PEOPLE. I IMMEDIATELY RECALLED THE FATAL MIDAIR IN EUROPE; AND HOW IT WAS CAUSED BY ONE OF THE CREWS LISTENING TO ATC; RATHER THAN THEIR TCASII. I STRONGLY FEEL THAT THIS TOPIC SHOULD CONTINUE TO BE EMPHASIZED IN OUR TRAINING SYS; TO INCLUDE THE MIL AVIATION COMMUNITY. WHEN THE CLOSING VELOCITY OF 2 ACFT IS 1000 MPH OR MORE; THERE SIMPLY IS NO WAY ATC CAN REACT TO THE ABOVE SCENARIO IN SUFFICIENT TIME. ONLY TCASII; WORKING AT THE SPD OF LIGHT; CAN HANDLE THE JOB. ALL PLTS SHOULD BE AWARE AND TRAINED TO RESPOND TO A TCASII RA; AND TO DISREGARD ATC IN THIS TYPE OF SIT.