And you're basically saying SR is falsified because an opponent of SR says it's falsified, when it's not.
No, not true. I say that it's falsified because Sagnac's experiment falsified it. Sagnac presents "Proof for the Existence of a Luminiferous Ether", and Einstein calls the luminiferous ether superfluous in his 1905 paper, and presents a theory which contradicts the existence of the luminiferous ether.
On the other hand your strange and incomprehensible reasoning is, that Einstein's Special Relativity could not be falsified by Sagnac as long as Struthio did not show how to explain the "discrepancy in the precession of the orbit of the planet Mercury".
I haven't forgotten the train example at all. And you've agreed already that the train example doesn't refute SR.
Yes, the train example is consistent with Special Relativity and does not refute Special Relativity. It's the Sagnac experiment which falsifies Special Relativity. And your recommendation to compare the train example with the Sagnac interferometer illustrates the falsification:
In the train example, the bolts arrive at Susan's place simultaneously and at Mary's place one after the other. In the Sagnac experiment, the detector shows that the beams arrive one after the other for every observer.
Sagnac is not a recent experiment. If it were recent, I could understand some debate over interpretation. But SR explained it over a century ago. There were SR explanations of the effect even before Sagnac's experiment. It's not as if nobody ever thought about it before.
The fact that you can't understand history is just a declaration concerning you're own ability to deal with reality. You can't use it in place of an explanation how Sagnac's result could be consistent with Einstein's idea that the speed of light is constant in all reference frames.
Sagnac simply disproves Einstein's postulate, and your comment is: That's impossible because then my understanding of how the science establishment works is wrong.
The pulses go in different directions the same distance. Observer M receives these pulses at different times. Does that really sound synchronized from M's perspective?
The question is nonsense. M knows that both beams are split from one of the same beam at the light source. He can reduce the radius of the loop to decrease the fringe shift, which, in the limit, shrinks to zero.