The only thing that matters is the direction from which the light is coming when it reaches the observer. It doesn't matter what distance it takes for the Sun's light to bend to horizontal, an observer at any point where it is horizontal will see the Sun as if it is level with them.
Yes, that means the direction must be parallel to the ground and at almost no height, so the bending point can not be above the atmosphere.
Let me explain :

Legend :
D is the sun
A is a point exactly below the sun at ground level
F is a point 500 miles high (edge of the atmolayer) directly below the sun
H is the point where light bends towards you
B you
a (line) the ground
e (line) the refracted sun light
The drawing is at real scale (x1000 in miles).
You can see that if the bend is not in the atmosphere, there is a 2,5* angle at witch you see the sun. It will never touch the horizon before disappearing.
This scenario is the best situation. If the bending point would be higher than that, the angle would increase and the sun will disappear even sooner before it hits the horizon. If the distance between where the sun is setting (point B) and where it is the middle of the day (point A) would be smaller, again the angle would increase. I chose the longest time possible for a day (12 hours) and the place where timezones are longest (the equator at about 1000 miles/timezone) hence 12.000 miles from A to B.
There are even more serious implications than this.
Notice point
I. If you were there and climbing up, you would gradually see the sun fading, because you reach the point where light is bent back. Where as in real life, when climbing you see more of the sun and the day lasts longer.
I actually calculated this. If you were 300 miles from where the sun is setting (roughly 25 minutes before sunset), and you were on a plane 8000 miles up it would be night, but on the ground it would be day. Just give a buddy of yous that's on the ground a phone call. You would have to be 8000 miles up, above the town of a buddy and the sun must have just set (for either of you, because this experiment can also be done above the point where the sun is setting). However this can be done without these hard to find circumstances, but you would have to know the speed of the plane and rate of assent.
Further, amateur rockets can reach 70 miles and often do. At this height the sun won't be visible even when on the ground it's 3 hours before sunset. We don't see that at all, on the contrary we see a lot more of the sun.
Another problem. If you are on a mountain and there are no higher peaks between you and the sunset, you can actually see the sun setting below you. Using simple tools you can determine that the angle is negative. This means the light is refracted up. How can the light be bent up towards you from a point 500 miles above you.
Also there are serious perspective problems. This light bending will have a lens effect, rendering the sun much smaller then it would be seen if the light was not bent. But more importantly because the vertical angle of refracted light is much grater than the horizontal one, it will render the sun as an ellipsis when it is not directly above.