There is no chance that this observation reflects neutrino physics. The neutrinps from supernova 1987a arrive 3hrs before the light, due to blocking of the supernova light by matter. Let us double this to 6hrs to include some dubious measurements, and assume that all the 6hrs is due to the superluminal neutrion travel. Then the time difference for 400km vs. 168,000 light years is $2.5 \cdot 10^{-12} s$, and this is 4 orders of magnitude smaller than the measured deviation. This means that if neutrinos outrun light by this much, the neutrinos from the supernova would have come in about a year earlier than the light.
The distance measurement is tricky, because the light-path is not the same as the neutrino path--- the neutrinos go through the Earth. If you measure the distance by sending radar between towers, you have to deal with curvature corrections due to mountains inbetween, buildings etc, which can easily add 20m of path-length over 400km. So I assume that they measured the distance using GPS. But then you have the issue that you are relying on U.S. government assurances that the absolute GPS positions are reliable to 20m. Relative distances might be ok even when absolute distances are off over large distances.
I can't say more without seeing the measurement, but it is certain in the scientific sense of 5 sigma confidence that this is not a correct result, so it is probably best to classify this as an irresponsible publicity stunt.
AFTER SKIMMING THE PAPER: No error bound on the GPS absolute position
Their estimate of distance measurements is based on the excellent relative values for displacement given the GPS coordinates. They can detect cm shifts in the Earth's crust etc. But the whole point is that you need the relative distance between the two points, and they have absolutely no independent calibration of the error in the long distance measurement, and blow smoke and mirrors with how accurate the short distance measurements are.
Here is the reference they give for their absolute distance measurement; they did none of their own; http://www.iers.org/nn_11216/IERS/EN/IERSHome/home.html , and they did no error estimate on the values they get from this. This is no good.
I don't know any way to calibrate the absolute position independently which is more accurate than the neutrino beam, so the best interpretation of the paper is that they used the neutrino beam to measure the distance between the recieving and emitting point with better accuracy than the project above gives.
Satelite Abberation
Given that the Earth is rotating with a speed v of approximately 400m/s, there is an abberation in the apparent angular position of satellites which is of the order v/c, and is normally negligible. The magnitude of the abberation between two instantaneous measurements 700 km apart depends on the angular position of the satellite in the sky, and for a satellite at 20,000 km gives a difference in estimated position of about 20m, times a trigonometric factor which can reduce this by 10% to 1%.
I don't see an estimate of correction for angular abberation in the paper.