I was never a particularly good physics student.
But I wonder if you could look at it in a different way, that does see the separate detections at widely separated points on earth as being separate photons. (In particular, if I recall correctly, the experiments that showed that a wave function of a particle interferes with itself were based on measuring the spatial distribution of SINGLE measured absorption events, after passing through slit(s), NOT of pairs of closely correlated absorption events, as in this case.)
Because of the distance, these stars do not appear very bright at the earth - i.e., there is a very low number of photons/short time interval at any given approximate wavelength arriving at earth. In addition, if they both hit the earth from a great distance, the two photons must have been emitted at nearly the same angular direction. In addition, it is possible (I'm not sure), that the selection used in astronomical interferometry that looks for correlated photons also attempts to find photons that arrive with approximately the same polarization. That is a lot of coincidence, but one that is more likely to occur if the two photons have some type of common originating event - i.e., something like a stimulated emission event. (Because stimulated emission events do tend to produce photons that are emitted at about the same time, in about the same direction, with about the same wavelength, phase and polarization.) (If there are any such experiments that look for MORE than two simultaneously correlated absorption and/or detection events, the probability that those photons have a common origin event of some type becomes even higher.)
In brief, since astronomical interferometry specifically selects for detection events that are correlated, there will of course be a strong tendency for them to have a common origin. That doesn't necessarily imply that all or most distant source light is coherent - it implies that these experiments are taking a very statistically biased sampling of dual absorption events, by looking for common timing, wavelength, angular arrival, and possibly, polarization - and that the statistically biased sample tends to have coherent detection pairs. 70
And that all that correlation, in my interpretation, tends to imply that the two photons in each pair frequently share a common origin event.
Remember, though, if my very poor understanding is correct, that quantum mechanics doesn't really tell you exactly what is true in nature - in fact, such exact underlying truth is not supposed to be physically determinable. Instead, the whole point of quantum mechanics is merely to attempt to predict and/or quantify the statistics of measurement. E.g., if you measure two photons with all those similar properties arriving from a distant star, all that earth-bound measurement does is tell you that they have a high probability of being measured with substantial phase coherence too. That measurement doesn't actually prove why it occurs - you could come up with different underlying physics explanations, but it might be hard to prove that any one explanation was true, in any specific instance. The best you can hope for is that the statistical distribution of measurements is better modelled by one explanation than another.
I would love to see what someone with a better understanding of quantum physics and astronomical interferometry would say about my explanation. :) I have wondered about the related issues ever since I read in an electrodynamics text that near-point sources of radiation tend to produce correlated photons; the textbook stated it was true, but gave no explanation. In my mind, I came up with the idea that it had to do with a high probability of stimulated emission events in near-point sources, but I never asked a professor if that was right.
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