I imagine the achievement here is mostly in the success of improvements to telescopes, AO, spectrographs and such which were necessary to raise SNR sufficiently so that valid data can be obtained in this particular difficult case. Galactic core is heavily obstructed by dust and gas.Why (or how) is this different than the Pound-Rebka experiment? (done 59 years ago)
But future quantum gravity theories are expected to differ from GR at field strengths (or curvatures, if you will) _much_ higher than even those at BH event horizons.Each new proof of GR necessarily puts a hard experimental limit on the kinds of theories that can replace it.
The disproved theories in question are not "theories of everything" you mentioned earlier, i.e. quantum mechanical unifications of SM forces with gravity.I think we are in agreement here. Some of the current theories have to be or have been discarded because they failed to predict what has been measured.
This paper talks about binary pulsars (circa 2008) and how experimental results have confirmed GR and limited other alternatives to GR:
https://books.google.com/books?id=sT_ICgAAQBAJ&pg=PA225&lpg=PA225&dq=GR+experiment+limits+alternate+theories&source=bl&ots=fFcBpAKvnS&sig=7XeNlFIe-Q-SQCkS7ppedB-ALc4&hl=en&sa=X&ved=2ahUKEwjTg7WisL_cAhWI7IMKHbZqAO0Q6AEwBnoECAUQAQ#v=onepage&q=GR experiment limits alternate theories&f=false
But it's not all that extreme. The acceleration due to gravity on S2 is about the same as on the surface of the moon. If you want to argue that what matters is potential, not force, you can do ~50x better with the white dwarf data.My guess is primarily because it was done at larger scales and more extreme conditions around a black hole whereas Pound Rebka was done in an Earth laboratory.