NON TWR ARPT; ACFT EXECUTED GO-AROUND BY DIRECTLY OVERFLYING SMT EXITING THE RWY.

Narrative

I WAS THE CAPT OF FLT FROM MCL TO JLN. WE WERE ON A IFR FLT PLAN WITH KANSAS CITY CENTER. AT ABOUT 35 MILES FROM THE ARPT WE REQUESTED LOWER; AND CENTER GAVE US A DESCENT TO 4000'. WE THEN DESCENDED FROM 11000' TO 4000'. WHEN WE WERE 25 MILES FROM THE ARPT WE HEARD CENTER TALKING TO A SMT WHICH WAS 6 MILES FROM THE ARPT. THE SMT THEN CANCELLED HIS CLRNC AND CENTER ADVISED US THAT THE SMT WAS GOING TO LAND ON 13. WHEN WE WERE 20 MILES FROM JOPLIN ARPT WE CALLED CENTER; SAID WE HAD THE JOPLIN ARPT IN SIGHT. WE WERE THEN CLRED FOR A VISUAL APCH TO THE JOPLIN ARPT. THEN WHEN WE WERE ABOUT 12 MILES FROM THE ARPT WE CANCELLED OUR IFR FLT PLAN WITH KANSAS CITY CENTER. NEXT WE SWITCHED OUR RADIOS TO 119.8 AND REPORTED ON THE CTAF THAT WE WERE 10 MILES NORTH WEST OF THE ARPT ON A STRAIGHT IN FINAL FOR RWY 13. WE KEPT OUR RADIO ON 119.8 AND HEARD NO OTHER ACFT CALL. WHEN WE WERE 5 MILES OUT; STILL ON FINAL APCH WE CALLED AGAIN; ADVISING TFC THAT WE WERE ON A FIVE MILE FINAL FOR RWY 13. WE THEN CALLED OUR POSITION ONCE MORE ON A ONE MILE FINAL. ALL THIS TIME WE DID NOT HEAR ANY OTHER ACFT ON THE FREQ; NOR DID WE SEE ANY ACFT. MY FIRST OFFICER AND I BOTH THOUGHT THE SMT MUST HAVE LANDED AND TAXIED IN ALREADY. HOWEVER; ON OUR LNDG ROLLOUT A PASSENGER SAW THE JET FLY OVER US FROM LEFT TO RIGHT. A COMPANY AGENT ALSO SAW THE SMT FLY OVER US. I WAS LATER ADVISED THAT THE SMT FLEW APPROX 20' OVER US. I WAS ALSO ADVISED THAT INSTEAD OF BEING ON THE CTAF THE SMT WAS TALKING TO FBO ON 122.95. FBO ADVISED THE SMT TWICE THAT HE SHOULD BE ON 119.8; THE CTAF. AFTER WE TAXIED TO THE GATE WE FOUND OUT WHAT HAD HAPPENED; SO WE LEFT OUR BATTERIES ON; ALONG WITH THE RADIOS. I WAS HOPING TO TALK TO THE SMT TO FIND OUT JUST WHAT HAPPENED. THE FIRST TIME MY F/O AND I SAW THE SMT WAS WHEN HE RETURNED TO LAND AGAIN. WE STILL HAD OUR RADIOS ON AND WE HADN'T HEARD THE SMT REPORT ANY OF HIS POSITIONS; NOT EVEN AFTER LNDG AND CLEARING THE RWY. TO AVOID THIS NEAR FATALITY IN THE FUTURE; JOPLIN; MO MUST GET AT LEAST A PERSON IN THE TWR TO RUN AN ADVISORY FREQ TO ACFT. IT WOULD BE BETTER YET IF THEY HAD A FULL-TIME CTL TWR. I ALSO FEEL THAT THE PLT OF THE SMT THAT ALMOST HIT US SHOULD NOT BE FLYING. HE HAS BROKEN THE FAR'S OF FLT PLANNING IN NOT KNOWING WHAT RADIO FREQ HE IS SUPPOSED TO BE ON. TODAY WAS JUST CLOSE.