It seems there may be some confusion in the question. I'm not aware of any statements by Edward Witten, a prominent theoretical physicist, suggesting that the constancy of the speed of light in the special theory of relativity or the principles of general covariance and the equivalence of inertial and gravitational mass in the general theory of relativity are not a priori.
The constancy of the speed of light in vacuum is a fundamental postulate of the special theory of relativity, introduced by Albert Einstein in 1905. It states that the speed of light in a vacuum is the same for all observers, regardless of their relative motion. This principle has been extensively tested and confirmed by numerous experiments.
General covariance is a fundamental principle in general relativity, which states that the laws of physics should have the same form in all coordinate systems. It allows for the description of gravity as the curvature of spacetime, with the motion of objects influenced by the geometry of the spacetime they inhabit.
The equivalence principle, another fundamental concept in general relativity, states that the effects of gravity are indistinguishable from the effects of acceleration. It implies that the inertial and gravitational masses of an object are equivalent, meaning that all objects fall in the same way in a gravitational field, regardless of their composition.
These principles are central to our current understanding of physics and have been validated by a wealth of experimental evidence. While it's always possible for scientific theories to evolve or be refined with new discoveries there is no widely known suggestion by Edward Witten or any other notable physicist challenging the a priori nature of these principles in the respective theories of relativity.