MULTIPLE RWY OP INTERSECTING RWYS SMA X HAD NMAC LTSS FROM SMT Y. SYS ERROR.

Narrative

SMA X WAS CLRED FOR A STRAIGHT IN 'OPTION' ON RWY 28R AND EXECUTED A TOUCH-AND-GO. SHORTLY AFTER ROTATION; WE RECEIVED A HURRIED ADVISORY FROM THE TWR ADVISING US OF TFC ON SHORT FINAL ON RWY 24; THE TOUCHDOWN END OF WHICH IS PERHAPS 100 FT SW OF THE DEP END OF 28R. I LOOKED TO MY R AND SAW SMT Y PASS PERHAPS 75 FT BELOW US. I ESTIMATE OUR ALT AS 150 AGL. WE NEVER SAW THE OTHER ACFT UNTIL IT WAS TOO LATE TO TAKE EVASIVE ACTION. WE CONTINUED OUR FLT BACK TO OUR HOME ARPT; AND UPON OUR ARR FOUND A MESSAGE ASKING US TO CALL THE CTL TWR. THE SUPVR ON DUTY ADVISED THAT THE OTHER PLT WAS FILING A NEAR-COLLISION RPT AND NEEDED CERTAIN INFO FROM US. I HAVE SINCE RECEIVED 2 MORE PHONE CALLS FROM THE TWR ASKING ME TO ELABORATE ON WHAT HAPPENED. THIS WAS A CTLR ERROR: 2 ACFT WERE CLRED INTO THE SAME SPACE AT THE SAME TIME. WE HAVE LEARNED THAT THIS WAS A TRAINING CTLR; AS WE SUSPECTED; SINCE THE 'SHORT-FINAL' ADVISORY WAS A DIFFERENT VOICE. THE RELATIVE POS OF THE 2 ACFT MADE IT VIRTUALLY IMPOSSIBLE FOR US TO SEE THE OTHER ACFT; LNDG ON A RWY ONLY 40 DEGS DIFFERENT THAN OURS WITH A FASTER GND SPD APCHING FROM BEHIND. WITH THE BACKGND LIGHTS OF THE TERMINAL BUILDING; WE WERE PROBABLY DIFFICULT TO SEE TO THE OTHER PLT AS WELL. I'M NOT SURE; THEREFORE; HOW THE PLTS COULD REASONABLY HAVE AVOIDED THIS CONFLICT. PERHAPS A BETTER 'BIG-PICTURE' MENTALITY WOULD HAVE HELPED -- TO LISTEN MORE CAREFULLY NOT ONLY TO CLRNCS DIRECTED TO US; BUT TO OTHERS OPERATING IN THE AREA; AS WELL. SUPPLEMENTAL INFO FROM ACN 206680: SMT Y WAS CLRED FOR A VISUAL APCH TO RWY 24 BY LANSING APCH CTL. WHEN HANDED OFF TO LANSING TWR; I INFORMED THEM THAT I WAS ON A VISUAL APCH TO 24. FURTHER IN; I WAS REQUESTED TO SQUARE OFF MY BASE LEG FOR TFC ON PARALLEL 28R; WHICH I DID AND DOUBLE-CHKED I WAS REDUCED TO MY FINAL APCH SPD OF 120 KTS. DID NOT HEAR FROM TWR AGAIN UNTIL THEY ASKED IF I HAD TFC; BEFORE I COULD ACKNOWLEDGE THIS; IT PASSED IN FRONT VERY CLOSE. THE PAX IN BACK SAID I DUCKED AND PUSHED THE NOSE DOWN; BUT THAT WAS JUST A REACTION BECAUSE IT WAS TOO LATE FOR EVASIVE ACTION. THE WX WAS CLR AND I NEVER DID SPOT THIS ACFT BEFORE THE NEAR MISS. WAS TOLD LATER THAT IT WAS A TRAINING ACFT WITH AN INSTRUCTOR. I DID RPT THIS INCIDENT TO THE LANSING TWR SUPVR ON DUTY; HE TOOK MY STATEMENT AND SAID HE WOULD FILE A RPT.