Ray,
After further reading I should add that it does not appear that the Italian researchers were responsible for the media hype. They posted their initial observations on ArXiv and the media ran with it. They have stated that they are still skeptical of the results and have asked for independent verification. It has spawned, as of this morning, 24 papers on ArXiv.
One paper questions whether they took into account the Coriolis Effect on the southeast traveling neutrino chain. That author did some admittedly quick and dirty calculations and that brought the arrival time back into the Uncetainty Principle range (+2 ns rather than +62 ns).
http://arxiv.org/abs/1110.0392
Another possibility that I didn't see in the papers (though it could be there) is the possibility that the two clocks (CERN and Gran Sasso) do not share a common rest frame. Gran Sasso Labs is SE of CERN. Gran Sasso, being closer to the rotational equator than CERN has a greater angular velocity than CERN. The Gran Sasso clock would be running very slightly slower than the CERN clock. 62 ns slower? I don't know. But it would run slower.
The idea that an FTL neutrino might open the possibility of time travel has some problems in itself. If the neutrinos do indeed travel faster than the speed of light, because they do have some minute rest mass, then the very theory that postulates relativistic time travel is falsified. Special Relativity would have to be completely re-worked and if there actually is no maxima for velocity then there is no relativistic time travel.
And last (though I'm preaching to the choir here) we have to be careful about stating that Special Relativity postulates time travel into the past if we exceed the speed of light. The Lorentz Transformation for FTL massive particles doesn't quite state it that way.
The Lorentzian gamma factor is defined as:
gamma = sqrt (1-v^2) where c=1
If v (the velocity of the object) is greater than c (greater than 1 - for the sake of the problem let's say it is 2, twice the speed of light) then we have:
gamma = sqrt (1-2^2) = sqrt (1-4) = sqrt(-3) ~= 1.73
i and -1.73
i
That doesn't state that time (if we are applying the gamma to the time factor) is running in the negative direction. It states that the gamma factor for time is imaginary, the squareroot of minus 3. The imaginary time coordinate is running orthogonal to our ordinary time coordinate - whatever that means (other time can be defined as a two dimensional coordinate space).
So running the clock backwards, if it is possible, is somewhat more complex than it appears. Might explain why physicists have to go to school for a few years more than 4. It might take a "couple of days" or more for them to wrap their heads around the concept of imaginary time and what it means in the real world.