CARJ FLT CREW INTERCEPTS RWY ILS FOR RWY 36L AT CVG DURING A NIGHT OP ALTHOUGH ATC CLAIMS THE VECTORS AND CLRNC WAS FOR RWY 36R.

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WE WERE ON THE CINCE 4 ARR. ON INITIAL CONTACT WITH CVG APCH CTL; WE WERE ASSIGNED ILS RWY 36L APCH. WE SET UP AND BRIEFED THE ILS TO RWY 36L. WE SWITCHED COM RADIO FREQS ONCE AND PERHAPS TWICE BEFORE BEING CLRED FOR THE APCH. WE ARE SURE THAT NONE OF THE CTLRS ADVISED US OF A RWY CHANGE. WHEN WE WERE GIVEN A 330 DEG HDG AND CLRED FOR THE APCH; I BELIEVE THE CTLR SAID RWY 36L AND I READ BACK RWY 36L. WE CONTINUED TO FLY TO INTERCEPT RWY 36L. AFTER WE CROSSED THE RWY 36R LOC; THE CTLR ASKED IF WE HAD INTERCEPTED THE RWY 36R LOC BECAUSE HE SHOWED US W OFF COURSE. I RESPONDED THAT WE HAD BEEN ASSIGNED AND CLRED FOR RWY 36L. THE CTLR THEN GAVE US NEW VECTORS AND CLRED US FOR THE ILS RWY 36R; WHICH WE COMPLIED UNEVENTFULLY. WE ARE CERTAIN WE WERE ORIGINALLY ASSIGNED RWY 36L AND THAT SUBSEQUENT CTLRS DID NOT CHANGE THE ASSIGNMENT. SO EITHER THE FINAL CTLR CLRED US FOR RWY 36R AND NEITHER PLT NOTICED THE CHANGE; OR HE MISTAKENLY SAID RWY 36L WHILE HE THOUGHT WE WERE GOING TO RWY 36R. WHICH OF THESE OCCURRED; WE ARE NOT SURE.