It shouldn't. Moving from B to A slower than light is possible*, moving from A to B faster than light isn't, and you can't change whether something is possible by changing reference frames.
*(Under special relativity without tachyons)
What I'm trying to get at is, What does a physicist mean when she says she saw X move from A to B faster than light? The measurement is made from a single point; say A. So the physicist is at A, sees X leave at time tX, sends a photon to B at time t0, and gets a photon back from B at time t1, which shows X at B at some time tB. I'm tempted to set tB = (t0+t1)/2, but I don't think relativity lets me do that, except within a particular reference frame.
"X travelled faster than light" only means that tX < t1. The FTL interpretation is t0 < ...
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.