Imagine an ant standing on some random point on a soccer ball in the middle of a field. Now rotate the ball so where the ant is will be directly facing the side of the field, 90 degrees rotation of the ball from facing either goal. At this specific point the ant can see each goal at each end of the field even though the ball is directly between the middle of the two goals. Well, depending how tall the ant is given the goals are so close to the ball.

A huge distance is actually a helping factor in this case. A 1.75 meter person can see 4,700 away before the horizon curves out of view. That means (ignoring the bending of light by the atmosphere still) the viewing angle allows for 1 meter "down" every ~2,685.7 meters out. The radius of the Earth is ~6,371,000 meters so to be able to see the middle of an object from ~the radius of the earth "down" with that viewing angle would require the object to be a minimum of ~2,685.7 * 6,371,000 = 17,110,594,700 meters away. That's a minimum distance of ~0.11 AU so the person would only get a partial view of the moon but a full view of the sun because the moon -isn't- far enough away! Well technically the Earth could rotate slightly farther while having the middle of the sun still visible but I'm too lazy to calculate if it's actually enough, my hunch is no. If you wanted to see the middle of the moon and the middle of the sun (with no bending by the atmosphere) during an eclipse you'd have to be near the top of Everest while it happens to be exactly rotated between each.