The 'thinness' of the sun's atmosphere would depend on a lot of factors, such as how much turbulent activity there is on the sun kicking mass off the surface, also the sun has a much larger diameter and although this atmosphere is thin, there is a lot farther to travel through it.
The 1.3 protons/cm^3 is the density of the solar wind headed to the Earth from the sun and NOT the density of our sun's atmosphere. That was just the amount of mass in space headed to the Earth in the solar wind (on that particular day).
As for achromatic abberation, i think this might apply to solid materials as lenses. I watch the sun go down over the ocean and when the bottom of the sun appears to touch the horizon, the top of the sun in reality has already gone behind the horizon; and if i put sunlight through a prism i see the rainbow ... achromatic abberation ... however i don't see this happen at sundown so I guess achromatic abberation does not apply if you are 'in' the lens, and since i have not viewed the sun after it has passed through the atmosphere and back out I really don't know if it experiences achromatic abberation after passing through our atmosphere and then back out into space. Does anyone else know about this? But if this WERE the case, has anyone actually looked at the plates during solar eclipse proving einstein's theory and analyzed them to determine if there were any signs of achromatic abberation present?
Don't get me wrong here. I do not suggest that the theory of relativity is wrong. I simply want to know if there are other factors in play in the proof that could slightly 'skew' the results. The physics of a star are complex, for example recent observations where mass falls back to the sun ...
http://www.spaceweather.com/archive.php?month=09&day=29&year=2008&view=view
Read the article about 'Great Prominence' and there you will find the following statement ... "No one understands why the top of the prominence cascades down as fast as it does; the 'magnetic diffusion coefficient' of the medium shouldn't allow it. At the same time, swirls and vortices indicate an exquisite degree of magnetic control so far impossible to duplicate in Earth laboratories. How does the sun do these things? It's a beautiful mystery."
The same or other forces at work around or on the sun could possibly account for other phenomena. What I am trying to point out here is that there may be many effects around a star that could to some degree or another affect passing light that are not yet fully understood.