Unless there is a CVR in that model of Hawk, we may never know. I can’t imagine that the Blackhawk crew would be unaware of DCA airliner ops with approaches to RW 1 that end up circling to RW 33. These helos, military and civilian, fly these routes nearly daily. And an LAO, or Local Area Orientation, is required to operate not only on these routes, but inside the airspace, with as many different areas of airspace and the constraints of the special use airspace there. It was a pain in the ass for me to be able to fly there for my missions, but I understood why it was necessary. Plus, the controller, if solo and working two freqs, would’ve been able to be heard what instructions he was giving to the airliners, even if perhaps the Hawk crew couldn’t hear the responses if they were on the helo freq, due to simulcasting. Unless there was some major distraction of some kind in the cockpit, which is entirely possible, spotting the wrong aircraft seems far more likely, but none of this will be known without a CVR from their bird.