this experiment assumes spherical geometry to calculate "real positions" of stars.
ie. It uses the Earth's radius, lat/long conversions to determine where a star "really is."
so you see when the star is observably occluded and calculate it's "true position" (based on spherical geometry)
and theres a difference between the two, which is traditionally explained by atmospheric refraction.
iow, they say the apparent position of a star is true on a flat earth but wrong if on a globe.
if you perform an experiment in this way
you've either baked spherical geometry into your reference point (the "real star position" that refraction is needed to explain)
or your using the apparent position as your reference and are assuming refraction doesn't exist.
either way the experiment doesnt prove ANYTHING AT ALL because its not independent of either model.
somebody doesn't understand logic and has too much time on their hands.