What a satellite can see also has to do with its orbit altitude. The ISS is in low Earth orbit. From its altitude at 52 degrees inclination, when it is at its northern most point in its orbit, it can see to its visible horizon which will be something above 52 degrees to something below 52 degrees (lets say 72 to 32 degrees latitude as rough numbers and avoid the math) and something similar in longitude for its present position. Its a spot on the Earth of roughly 20 degrees Earth angle in radius that is moving with the satellite in orbit.
At higher altitude the spot size (visible horizon being farther now) is much larger. A geosynchronous satellite at the Equator (which is where this satellite was headed) can see roughly up to 65 or 70 degrees in latitude and down to -65 or -70 degrees latitude, and cover a similar swath in longitude, which is a good chunk of the Earths surface.
Hope this helps.
But you've lost the original discussion point. We weren't talking about what a satellite could potentially see but how much of the earth would be beneath the orbit trace. At least I was. Perhaps we are just providing answers to two different questions.
Enjoy the rest of the day.