I'm told Einstein leans heavily on Riemann geometry for General Relativity (and perhaps alternative geometries like Riemanns make sense if gravity curves space-time) but until/unless we have a lot more experimental data on Relativity I'm not prepared to say it just LOOKS that way because we're missing something. Beyond that, sure, if you change an axiom you change everything built on it (in a way, that's the point) but if it's just an arbitrary change that creates a false statement it's just contrariness, not philosophy. I can say the Moon's made of green cheese or that man never walked on it if I'm feeling obstinate, but no reasonable person will entertain either notion.