Is General Relativity Generally Relativistic?

Within the lore of nearly every scientific theory, among the facts, laws, theorems, and such that constitute the “truths” it expresses, are one or more principles. Physics textbooks, I know, usually mention them at the beginning, or during some interlude given over to general remarks or speculation. As examples, the uncertainty principle and correspondance principle of quantum mechanics come to mind (see, e.g., Messiah 1960). And associated with the general theory of relativity, which is particularly rich in principles, are a principle of general covariance, a principle of equivalence (or two), Mach's principle, and a general principle of relativity (see, e.g., Misner, Thome, and Wheeler 1973). Where do principles come from? Generally, as I said, they are supposed to be “truths” about the working of the world: observations and experiments are appealed to as their sources. But this doesn't distinguish them from facts and laws.