Quotes from the news wire:
Einstein's right, at least for now, we can absolutely rule out Newton's law of gravity. Our observations are consistent with Einstein's theory of general relativity. However, Albert Einstein theory is definitely showing vulnerability. It can not fully explain gravity inside a black hole, and at some point we will need to move beyond Einstein's theory to a more comprehensive theory of gravity that explains what a black hole is.
What's so special about S0-2 is we have its complete orbit in three dimensions, that's what gives us the entry ticket into the tests of general relativity. We asked how gravity behaves near a supermassive black hole and whether Einstein's theory is telling us the full story. Seeing stars go through their complete orbit provides the first opportunity to test fundamental physics using the motions of these stars.
We're learning how gravity works. It's one of four fundamental forces and the one we have tested the least, there are many regions where we just haven't asked, how does gravity work here ? It's easy to be overconfident and there are many ways to misinterpret the data, many ways that small errors can accumulate into significant mistakes, which is why we did not rush our analysis.