Any scientific theory is based on the scientific method:
"Four essential elements of a scientific method are iterations, recursions, interleavings, and orderings of the following:
Characterizations (observations, definitions, and measurements of the subject of inquiry)
Hypotheses (theoretical, hypothetical explanations of observations and measurements of the subject)
Predictions (reasoning including logical deduction from the hypothesis or theory)
Experiments (tests of all of the above). from http://en.wikipedia.org/wiki/Scientific_method#Elements_of_scientific_method
We begin with observation, we end with observation. The circle must be closed. If something escapes from observation, the scientific method cannot apply and there is no proper theory.
Relativity is based upon observation: C the speed of light is both a measurement and an axiom. And Relativity is supported by observational experiment. The circle is closed, everything goes well, Relativity is a Theory.
But if Mother Nature was more tricky than we thought, and if something bizarre happened in what we call "observation", the tricky part would be hidden both in the axiom and in the experiment. Even in this case, the theory could work, the circle would still be closed, the "tricky error" would be "outside" the theory, and we would never be able to notice anything of it. Everything would be explained perfectly, mathematically, but not necessary the way it really works.