It had damn well better be checked that way, because it rests on the assumption of flat space, which may or may not be true. The derivation from the axioms is not checked by empirical data; the axioms themselves are. If you don't check the axioms, you don't have knowledge, you have pretty equations on paper, unconnected to any fact. Pythagoras is just as much empirical knowledge as Einstein; it's just that the axioms are closer to being built-in to the human brain, so you get an illusion of Eternal Obviousness. Try explaining the flat-space axioms to squid beings from the planet Rigel, which as it happens has a gravity field twenty times that of Earth, and see how far you get. "There's only one parallel line through a given point", you say, and the squid explodes in scorn. "Of course there's more than one! Here, I'll draw them for you and you can see for yourself!"