I am not convinced that one can measure 58 billionths of a second accurately. I am also not convinced speed of light is constant. Everything in life fluctuates, why should light be exempt?
Scientists Report Second Sighting of Faster-Than-Light Neutrinos
(This is one of the reasons I'm a mathematician and not a physicist. I won't wake up one morning to learn that 50 years of my study has been for nothing.)
my model of reality is something like a Riemann surface. as long as we are only on "part" of the surface, it looks like one thing, if we move to another region of the surface, it may look like an entirely different thing.
i do not believe we will ever have an "ultimate theory of ultimate reality", but rather, several robust theories explaining large swaths of reality, but which do not appear to have a common "superset". i believe that which model of reality we choose, will prove to be scale-dependent.
if these results are to be believed, physicists have a choice: ditch some portion of relativity, or the standard model. i would argue for ditching the standard model, i believe our understanding of small-scale physics is not as good as large-scale physics.
there is some reason to believe that there is "some constraint" to how fast things can travel. assigning that constraint to the speed of a photon in a vacuum (if indeed a vacuum really does exist), may be unrealistic. the down-side to this, is that our classification of sub-atomic particles may not obey the symmetry rules we thought they did. but there are lots of possible symmetries, the possible combination of Lie groups is very large, so we need not, for example, abandon all hope that some other symmetry structure with perhaps more complexity, governs.
i do not subscribe to the notion that mathematics is "ultimately true". there are certain reasons we pick the logical structures we do: our brains are "pre-wired" for logics of a certain sort. we can only imagine the things which make sense to us, there is no reason to believe that other ways of viewing things might not be possible. one could imagine an alien species for which a trivalent logic (for example) was as natural for them as a bivalent logic is for us. they might think our set theory is "quaint", and regard many of our logical paradoxes as non-problemmatic.
we carry our intuitions as baggage, as helpful as they may be (to us). objective reality (if indeed it exists) has no such need, and is quite likely to continue to display behavior that surprises us. our guesses that infinite things DO exist (or at least "could"), or that topological completeness "DOES" occur, or that choice functions CAN be made, could all prove to be wrong, or only "partially (context-dependently)" true. we are, of course, hopeful that much of our mathematical knowledge will still be a fruitful way of looking at the world far into the future, but there is no guarantee of this, not even logical consistency gives a mathematical system immunity to modification (think of euclidean versus non-euclidean geometry).