The link above is of a private weather baloon launch tp 35 km. It uses 120 degree wide angle lense, and when that distortion is accounted for, there is no curve at all.
Care to explain?
Well, for starters, that is only 35 km, not 35 000 km.
But how did they correct for it?
The simplest automated method will look for a line which it presumes it straight and straighten it out. So that will remove any curve.
To do it honestly, you nee to know where the centre of the lens is and a bunch of details about the lens.
To analyse it without that you need Earth to be moving around the frame, not just staying at roughly the same point. You need it to move from one side of centre frame to the other (note: side here doesn't mean left to right, it is whatever direction the horizon is, so up/down works as well.
A key thing to look for is where the horizon appears flat. Is it at centre frame, with the horizon on the same side as the centre of Earth, or the opposite side.
It is even better if the camera is rotating around as well, so Earth's centre is on opposite sides as well. Then you can compare what happens from different directions to determine where the centre of frame is, or just look to see if it is always flat in the same spot.