Sometimes this is what is meant instead...a simple magnification effect:
http://wiki.tfes.org/Magnification_of_the_Sun_at_Sunset
This is very irrelevant. We are talking about apparent position right now, not apparent size.
In any case I'll address this,
While I don't disagree that magnification can occur, it would not be able to compensate for how much smaller the sun would actually be from that great a distance.
Suppose a 32 mile wide sun is 3000 miles above earth and the sun is 10,000 miles away at sunset.
This sun subtends at an angle of 5° when it is overhead. It also subtends at approximately the same value while at sunset. So this means that this magnification effect would have to compensate for however much smaller the sun should appear to get after it has traveled away 10,000 miles.
The pictures in the wiki are not convincing.
For them to be consistent with the argument Rowbotham is proposing, then the headlights would need to appear to be the same size no matter how far away they get from the observer, much like the sun. Instead the picture shows the headlights gradually getting bigger about halfway back and then getting smaller again further away.
Why on earth would the wiki show an example that is nothing like what they are suggesting?
Also, this example (although erroneous), only seems to apply to object that are radiating light. The principles of refraction apply not just to the sun. I simply chose the sun as the subject here. All of this also applies to any object that disappears below the horizon (IE. all objects).