I'll try to make some sense. It's due to the way that the camera is angled. For example, take a basketball. Now, just hold it a food in front of you and look directly at it. It's the line is not that large, and the basketball clearly curved. Now, hold that basketball up to your eye, and make sure one of those block lines is on it, and focus on whatever is behind it or the top of the ball, using your peripheral vision to see the ball. If you did it correctly, the black line will appear larger, and you'd clearly see the ball was still curved, but not as curved as it was a foot away.

Now for the curvature, the closer you are to the ball the less of a curve you'll see, and curves become more prominent the farther away from the ball you are. Move the ball just an inch from your face and the curves keep getting more prominent. For your argument that you're not going to see a curve then a distinctive one out of nowhere, at sea-level, we see a slightly tiny curve, almost nothing at all, now, let's go up 20 mi to your balloon and you can clearly see that there's a curve. So, even 30 miles above a position will make a curve more prominent.

The ISS maintains an orbit of around 200-250 mi, and I'd say this is a little bit on the lower side. That's around 180 miles higher than that balloon. The picture makes it look much larger because of the angle it was taken.

There's probably someone who could make much more sense out of it than I, but I'm just giving my reasoning for the photo.