FLT CREW OF B767-300 NEARLY CROSS ACTIVE RWY 36L AT CVG; CAUSING CARJ ON APCH TO GO AROUND.

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AFTER PUSHBACK AND ENG START WE RECEIVED TAXI INSTRUCTIONS FROM GND CTL TO ENTER TXWY K AND TO HOLD SHORT OF RWY 27 AT INTXN K; E. AS I WAS SLOWING; APCHING THE INTXN; SIMULTANEOUSLY CVG GND CTL CALLS WITH FURTHER TAXI INSTRUCTIONS AS A FLT ATTENDANT RINGS THE COCKPIT WITH A PAX DOOR PROB. THE FLT ATTENDANT WANTED TO OPEN THE DOOR AND MY IMMEDIATE CONCERN FROM THE FLT ATTENDANT'S COM IS THAT SHE WANTS TO OPEN AN 'ARMED' DOOR WHICH MAY CAUSE A SLIDE DEPLOYMENT. THE COPLT INDICATES THAT WE ARE TO CONTINUE OUR TAXI AND I DO SO AS I AM TELLING THE FLT ATTENDANT NOT TO OPEN THE DOOR UNTIL WE COME TO A COMPLETE STOP. AS WE CONTINUED THE TAXI; WE ROLLED THROUGH THE K; E INTXN AS I THOUGHT WE WERE INSTRUCTED TO DO. THE NEXT INTXN APPROX 75 YARDS WAS INTXN K; D AND TXWY D IS THE PARALLEL TXWY TO THE RWY WE WERE TAXIING TO; SO I INTENDED TO TURN THERE AND PROCEED. AS WE APCHED INTXN K; D; GND CTL TOLD US TO HOLD POS. I STOPPED ACFT AT THE K; D INTXN. APPARENTLY CVG TWR THOUGHT WE WERE GOING TO CROSS THE ACTIVE AND SENT A REGIONAL JET ON A 1 1/2 MI FINAL AROUND. AT NO TIME DID WE CROSS OR INTEND TO CROSS THE HOLD SHORT LINE FOR RWY 36L. PROBABLE CAUSES TO THIS INCIDENT: SIMULTANEOUS CALLS FROM GND CTL AND ONBOARD FLT ATTENDANT; POOR TXWY SIGNAGE AT INTXNS K; E; AND K; D; AT CVG. SUPPLEMENTAL INFO FROM ACN 632739: THE NEXT THING I SEE IS WHAT LOOKS LIKE A RWY APCHING OFF THE NOSE (RWY 36L). PARALYZED WITH DISBELIEF; JUST AS I SEE THE HOLD SHORT LINE PASS UNDER THE NOSE; GND YELLS 'AIRLINE XX; HOLD! HOLD! HOLD!' THE CAPT SLAMMED ON THE BRAKES. THOUGH WE CROSSED THE HOLD SHORT LINE OF RWY 36L; WE DID NOT INFRINGE ON THE RWY ITSELF. THIS WAS THE LAST LEG OF THE LAST DAY OF THE TRIP AND THE ONE CLR THOUGHT I REMEMBER IN MAKING MY SUGGESTIONS WAS TO KEEP THE ACFT MOVING AS LONG AS WE COULD BEFORE WE STOPPED TO FIX THE DOOR PROB (GOT HOMEITIS) TO EXPEDITE THINGS. CLRLY; THIS IS A CLASSIC EXAMPLE OF DISTR; LACK OF ATTN; AND LACK OF COM. THE ONE HUGE LESSON THAT WAS HAMMERED HOME WHICH I SHOULD KNOW COLD...ANY PROBS -- STOP THE ACFT; INFORM GND.