Are they THAT sensitive? Possibly not.
In order for this to be from an error in measurement you need to be a few meters off (18 meters if that's the only problem). There are standard GPS techniques and surveying techniques which can be used to get very precise values. They state in the paper and elsewhere that they are confident to around 30 cm. Differential GPS can have accuracy down to about 10-15 cm, and careful averaging of standard GPS can get you in the range of 20 cm, so this isn't at all implausible but it is still a definite potential source of error.
A more plausible issue is that si...
http://www.nature.com/news/2011/110922/full/news.2011.554.html
http://arxiv.org/abs/1109.4897v1
http://usersguidetotheuniverse.com/?p=2169
http://news.ycombinator.com/item?id=3027056
Perhaps the end of the era of the light cone and beginning of the era of the neutrino cone? I'd be curious to see your probability estimates for whether this theory pans out. Or other crackpot hypotheses to explain the results.