Light Transport
Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Commercial
Situational Awareness; Communication Breakdown
ATC Issue All Types; Conflict Ground Conflict; Critical
Air Traffic Control Provided Assistance; Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action
Human Factors; Weather
We were taxiing for takeoff from the Ramp getting ready for takeoff. We held short of taxiway Sierra and contacted ground for taxi. CVG ground told us to hold position and we complied. A few seconds later the ground controller said 'Aircraft X; there is a 767 (Aircraft Y) that will be passing you from right to left heading north on Sierra. Give way to that aircraft and taxi; Sierra/Tango to [Runway] 36R.' We read back the instructions with no conflict. At that time; there was Aircraft Y immediately to our right passing right to left. We let him pass and started rolling onto Sierra southbound to 36R. The visibility was poor; 3/4 SM; but greater than 6;000 RVR. It had been raining all morning and the windows were foggy as well. As we rolled onto Sierra; the PIC noticed lights in the oncoming direction. After a few moments the flight crew realized that it was another 767 (Aircraft Z) quickly approaching head on. The PIC got on the radios and said 'the 767 heading north on Sierra needs to stop immediately' in which the other aircraft responded 'We're stopping.' ATC then got on the radio and asked if that was [callsign] who just said that. We responded in the affirmative. He then questioned us why we didn't wait for the 767 to pass us and the PIC responded that we did wait for the 767 to pass us; and that we were not aware that there were 2 767's on Sierra; and that the visibility was very poor. ATC did not ask for any more information.We were able to make a 180 degree turn and continue North on Sierra/T5/Tango to 36R. The flight continued with no further abnormalities. In the future; the flight crew could have been more aware of the situation by monitoring ground prior to holding short of the ramp to paint a bigger picture and improve overall SA (Situational Awareness). In addition; the flight crew must remind themselves to always be vigilant and hyper aware of their surrounds.
Air Taxi Captain reported a ground conflict due to a communication breakdown with ATC.