Of all the physical theories, general relativity is probably the one that's least likely to be true of. Because it just wasn't needed in all its generality at that point of time. Instead of going from first principles like Einstein some other physicist could have developed it from the other end, and made corrections to Newton mechanics based on the observed precession of Mercury and the deflection of starlight by the Sun (if someone would have done that observation without the impetus of GR). It could have been akin to how quantum theory in its first 25 years was a collection of ad-hoc explanations of various phenomena using the quantized energy idea but having no generalized theory of them.
We'd have found out for sure when we first built a GPS system without relativity correction. It wouldn't work and that experimental error would have to be explained somehow and that in turn would lead to the discovery of GR if it had not been discovered through some other means at that time.
