Yes, you did indeed see a curve and your photograph does indeed show a curve. The window in the airplane is curved to fit the body and this creates a convex lens that slightly distorts the image seen.
That may be true with some windows, but the curve when looking through a lens changes depending on the position of your head. Look at these different photos using different lenses:
As you can see, the two distorted wide-angle shots on the left show the curves on the top and bottom of the shot bending in opposite ways. By moving your viewpoint up or down (or your head up or down inside the plane), different parts of the image would bend more. Your theory of windows making the earth look curved doesn't make any sense.
The great thing about using distorted images is that you can twist them to fit any lie. An airplane window is not a perfectly level 8mm wide-angle camera lens. Angle those cameras a bit you've got a nice subtle curve to your horizon.