Date: 201509
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Flight conditions: VMC
Light: Daylight
Aircraft: Commercial Fixed Wing
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Takeoff / Launch
ATC / advisory: Tower ZZZ
Second aircraft: Commercial Fixed Wing
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Situational Awareness
Second reporter function: First Officer; Pilot Not Flying
Anomaly: ATC Issue All Types; Conflict Ground Conflict; Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy; Flight Deck / Cabin / Aircraft Event Illness / Injury; Ground Incursion Runway
Detector: Person Air Traffic Control; Person Flight Crew
When detected: In-flight; Taxi
Result: Flight Crew Requested ATC Assistance / Clarification; Flight Crew Took Evasive Action
Contributing factors: Procedure; Human Factors
Primary problem: Human Factors

Narrative: We were number one for departure on runway 17R. Tower called and cleared us for takeoff on runway 17R. She said 'RNAV NAVYE cleared for takeoff 17R'. We also heard her clear another aircraft to land on runway 17C. All aircraft lights were illuminated as we took the runway for departure. The First Officer cleared the right side of the runway. I said 'Clear Left' and we noted the aircraft on final for what we thought was 17C. With the angle; it was hard to tell he wasn't lined up on 17C. We were 3/4 of the way across the hold short line for 17R when we realized he was actually on final for runway 17R. I stopped the aircraft immediately and the First Officer got on the radio and announced we were on the runway...that we were not clear. We did  not have time to clear the runway before the aircraft flew by us and landed. It appeared to us that he leveled off and extended his landing. He never went around but someone on the radio stated; 'Don't worry guys...I've got it'.Had we not stopped the aircraft when we did; we would have been directly in his landing path and an accident was probable. There was never any urgency on the part of the controller to acknowledge or correct the problem. We asked to taxi clear of the runway and for a phone number to call the tower. Once clear of the runway with the parking brake set; I called the tower and talked with the supervisor. He said there was no problem as our aircraft nose was barely over the hold line. We were 3/4 of the way across the hold short line just short of the threshold paint when the aircraft went by us. We were not just over the hold line! The supervisor acknowledged that the controller had made a mistake. She had been given the flight; which was on a medical [urgency] and she did not realize he was landing on runway 17R. He also acknowledged that because of our actions; an incident was probably averted.Close runway proximity led us to believe the aircraft on final was on 17C. The controller had just cleared an aircraft to land on 17C and nobody had been cleared to land on 17R. The controller had been given the medical [urgency] flight and was unaware of their landing runway. The controller never told them to go-around; and they never initiated a go-around even after realizing we were on the runway. Better communication between the air traffic controllers. Runway 17R was being used for a medical [urgency] landing. No aircraft should have been cleared to takeoff until that aircraft was on the ground.


Second narrative: Better communication between the controllers and possibly the emergency aircraft. Maybe not allowing aircraft to depart during [priority] landing on runways that are close ie XXR/XXC; just in case the aircraft [in distress] lands on the wrong one.


Synopsis: A flight crew reported being cleared for takeoff with an aircraft on final for the parallel runway. As the crew crossed the hold line it became apparent that the other aircraft was lined up for the runway cleared for takeoff. The Captain on the ground stopped the aircraft and the Tower was informed of the situation. The other aircraft was allowed to land. Reports from the other crew are also included.