SABRELINER FLC ISSUED 'VISUAL SEPARATION' DSCNT THOUGH OPPOSITE DIRECTION TFC. OTHER TFC TURNED TO AVOID SABRELINER.

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WHILE ON DSCNT IN VFR CONDITIONS TO 15000 FT ON AN IFR FLT PLAN; ATC GAVE US INSTRUCTIONS TO EXPECT A DSCNT TO CROSS 30 MI FROM SUS AT 5000 FT. HE THEN ISSUED US A TA FOR A COMMUTER ACFT HEADING OUR DIRECTION 15 MI IN FRONT OF US AT 14000 FT; AND HE WANTED TO KNOW IF WE HAD HIM IN SIGHT. I REPLIED THAT I DID HAVE THE TFC. AT THAT TIME; WE WERE ISSUED A CLRNC TO MAINTAIN A VISUAL DSCNT WITH THE COMMUTER AND DSCNT TO 5000 FT BY 30 MI FROM SUS. I MAINTAINED EYE CONTACT WITH THE TFC THAT ONLY LEFT THEIR NAV LIGHTS ON. WE HAD OUR WINGTIP RECOGNITION LIGHTS; STROBE LIGHTS; NAV LIGHTS AND ROTATING BEACON LIGHTS TURNED ON. AS WE APCHED 15000 FT; WE MADE THE CHOICE TO DSND THROUGH THAT ALT TO 5000 FT; SINCE IT APPEARED THAT WE STILL HAD AMPLE SEPARATION DISTANCE. WE WERE DSNDING AT 4000 FPM; AND I COULD TELL BY WATCHING THE COMMUTER THAT WE PASSED THROUGH HIS ALT. AS WE WERE APCHING 13000 FT AND HE WAS PASSING OVERHEAD; I COULD SEE HE INITIATED A R TURN AND PROCEEDED TO QUESTION ATC FOR LETTING US HAVE THE DSCNT. I PRESUME THAT THE COMMUTER MAY HAVE HAD A TA ON THEIR TCASII SYS AND THOUGHT WE WERE TOO CLOSE. ACCORDING TO MKC ATC; THE COMMUTER SAID WE WERE ONLY 300 FT BELOW THEIR ALT. WITH OUR DSCNT RATE; I BELIEVE THAT THE TCASII ON THE COMMUTER WAS SHOWING A DELAYED ALT INDICATION DUE TO OUR HIGH DSCNT RATE; THUS WAS MAKING A FALSE PROJECTION. I ALSO BELIEVE THE PLTS OF THE COMMUTER WERE RELYING ON THEIR INSTRUMENTATION TOO MUCH; AND WERE NOT LOOKING OUT THE WINDOW. THE COMMUTER COULD HAVE HELPED US JUDGE THEIR DISTANCE VISUALLY BETTER BY TURNING ON MORE IDENT LIGHTS. THEY SHOULD HAVE ALSO BEEN MORE VIGILANT AND LOOKED OUTSIDE THE ACFT FOR US AND TAKE CORRECTIVE ACTION SOONER IF THEY HAD ANY CONCERNS AS TO OUR DISTANCE. BY THE TIME THEY HAD INITIATED THEIR TURN; IF WE WERE REALLY A THREAT; IT WOULD HAVE BEEN TOO LATE FOR THEM TO TURN. RELIANCE ON THE 'STATE-OF-THE-ART' TCASII ACFT EQUIP MAY NOT ALWAYS BE A WISE CHOICE. THE PLTS SHOULD BE MORE VIGILANT; AND MAKE SURE THEY KEEP 1 SET OF EYES LOOKING OUTSIDE THE COCKPIT AS A CONSTANT BACKUP TO THEIR INSTRUMENTATION. SUPPLEMENTAL INFO FROM ACN 568420: LATER; ATC CALLED AND SAID THEY HAD NO PROB; BUT WANTED TO KNOW HOW IT APPEARED TO US. WE DID HEAR THE COMMUTER DISCUSS THE ISSUE WITH ATC. I FEEL MAYBE AT NIGHT; VISUAL DSCNT WITH ONCOMING TFC MAY NOT BE A GOOD IDEA; AND THAT BOTH THE ACFT SHOULD BE AWARE OF EACH OTHER AS WELL AS MORE LIGHTING NEEDS TO BE USED FOR BETTER IDENT.