Tachyonic neutrinos can explain SN 1987A neutrinos beating photons to Earth, and tachyonic neutrinos can explain the CERN observations, but, critically, they cannot explain both phenomena simultaneously. The SN 1987A neutrinos apparently moved slower than the CERN neutrinos, when the pure tachyonic explanation would have them move faster than the CERN neutrinos.
This isn't to say neutrinos couldn't be tachyons, but it would still leave the CERN data requiring an explanation.
Your point is correct. But I'd also like to note that in case anyone thinks that SN 1987A is a problem for physics- the conventional model explains SN 1987A neutrinos beating the photos to Earth. Neutrinos are produced in the core of a star when it goes supernova. Light has to slowly works its way out from the core going through all the matter, or is produced at the very upper stages of the star. Neutrinos don't interact with much matter so they get to go through quickly and so get a few hours head start. Since they are traveling very close to the spee...
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.