LGT MAKES TKOF WHEN CLRED TO POS AND HOLD. CLOSE PROX WITH MIL FGT.

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WE WERE OPERATING AS A TAIL-END FERRY FLT (CHS-31J) AFTER A 41 HR; 5 DAY INTL OP. IFR CLRNC WAS RECEIVED BY THE FO JUST BEFORE REACHING CHS RWY 3. CLRNC WAS GIVEN BY CHS CTL TWR TO ENTER RWY 3. I UNDERSTOOD THAT TKOF CLRNC HAD BEEN ISSUED; THEREFORE FOLLOWED THROUGH WITH TKOF RUN AND LIFTOFF. AT 30-50 FT AGL; THE CTL TWR STATED THAT WE DID NOT HAVE TKOF CLRNC; THAT WE WERE CLRED FOR 'POS AND HOLD' ONLY. SIMULTANEOUS WITH THE CTL TWR VERBAL XMISSION; I OBSERVED A FIGHTER JET WHICH EITHER HAD MADE LOW APCH OR TKOF ON RWY 15. HIS POS WAS AT MY 1 O'CLOCK ORIENTATION AS WE BOTH PASSED APPROX 50 FT AGL. NO EVASIVE ACTION WAS REQUIRED AS OUR RESPECTIVE FLT PATHS WERE NOT IN CONFLICT. IT IS POSSIBLE THAT AFTER JUST HEARING 'CLRED AS FILED' AS PART OF THE IFR CLRNC READBACK; THIS I MISTOOK THIS AS CLRED FOR TKOF; AND INADVERTENTLY MADE AN ILLEGAL TKOF AS WAS INDICATED BY CHS CTL TWR. I WAS UNAWARE OF THE FIGHTER'S PRESENCE AND UNABLE TO HEAR HIS XMISSIONS SO I SUSPECT HE WAS UTILIZING UHF. A CONTRIBUTING FACTOR AND SURPRISE TO ME IS THAT THE CTL TWR ALLOWED OUR FULL TKOF RUN IF WE WERE NOT ACTUALLY CLRED FOR TKOF. A FULL COCKPIT AWARENESS AND UNDERSTANDING OF THE CLRNC MIGHT HAVE ALLOWED US TO AVOID THE ABOVE AND/OR CHALLENGE THE CLRNC IF IN QUESTION.