The second experiment with neutrinos has been done at LHC and it seems to imply the same thing (50 ns. δ t). I can't say for certain what the universe will do under every circumstance, but I can consider consequences and effects. The appearance of any super-luminary ( FTL=faster than light ) effects would have profound consequences in how we deal with the universe.
I wonder about how the experiment is implemented. If it feeds back on itself, any changes in time would be amplified. In any case it would create real problems with the whole world if it were discovered that real ( as opposed to virtual ) FTL communication were possible. Many people on Slashdot have posed the question about seeing neutrino bursts from distant supernova years before the events themselves and AFAIK, that does not happen. In addition, changes in the sun could be detected before they were seen by telescope, or cause disruption. Very hard to accept. If it were actually true, one could know before anyone else if a change in the world would influence a stock price and react 50ns before any other automated trading program to go short or long on an event. It would imply that a system of laser weapons would be obsolete, as it would be possible to communicate the path of the laser before it had effect. I think I would have to smoke a lot of neutrinos to believe that anything is FTL. It would allow the canceling of a radio signal before it was received. I can't say for certain what this universe will do, but I can see that if it were true, the world would be turned inside out in a nanosecond.
Independent of the FTL, there is something about neutrinos that makes them a game changer. If you are communicating through the Earth, it is possible to have a comm distance of d/Π, instead of d, or sometimes just the chord distance. Faster communication is always an advantage in every circumstance. It would seem that even though I don't accept that neutrinos are FTL, it does make some very interesting things possible in P2P communication. It does provoke some interesting thought on neutrino MiTMs. (Man in The Middle).
Maxwell's papers are interesting and they have sparked some new ideas. I also am wondering about the Schwarzschild radius and the big bang. If all the matter in the universe were inside the Schwarzschild radius, how exactly does that work? It seems to depend on imaginary physics that are untestable. I have developed a time within time program and perhaps it will give me some insight into why things are observed to act so oddly. Personally I would think that the neutrino experiment should be operated in a feedback loop and then it would produce results that dissolved the margins. Without knowing the detail of their implementation it isn't possible to speculate on a proper negative proof.
ADDED: As always, XKCD has the best take on those pesky things that violate all the prior measurements.