The line that runs just to the north of Midway Airport is owned by CSX, not 100% sure though. In the area, the transcon parallels I-55 to the north and the Chicago sub is about 3 miles north of the transcon. The Indiana Harbor Belt runs north/south just to the east of Midway and the BNSF Chicago sub and transcon lines connect with the IHB and the IHB connects with CSX just to the east of Midway.
The line that runs in a north-south alignment just E of Midway is not IHB, it is in fact the Belt Railway of Chicago, which is headquartered at nearby Clearing Yard, and David, the BNSF trains you saw were likely headed to/from there. BNSF and CSX, among others, do have trackage rights along this segment.
For additional clarity, the BNSF racetrack connects with IHB about a mile E of LaGrange Road (in fact, right next to the Congress Park Metra station), and the Transcon connects with IHB at McCook crossing, just a few miles west of BRC's Clearing yard...
