Your statistical fluke estimate is too high, experiment was repeated like 16,000 times.
Bear in mind that many parapsychological experiments have been repeated vastly more than that. My impression is that anyone who wants to argue that this is extremely unlikely to be a statistical fluke is going to have a much harder time viewing parapsychology as the control group for science.
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.