I don't think that Neutrinos have moved faster than the speed of light. There are lots of complications involved with the measurement of speed. They messed up the process of measurement. As far as I know, the only thing that could happen is neutrinos may have followed the straight path somehow not effected by the gravity. But I don't think it can be true. Even if Neutrinos are thought of being mass-less particles even though they have mass, gravity acts the same the way for unequal masses.
What they did is basic velocity measurement that we all know. The implementation is different. The velocity measurement is not so easy for neutrinos. They cant measure a velocity of single neutrino with their detector, they have to throw a whole lot of them at the detector. But they dont know when the neutrinos are created when they get detected. They analyzed the previous data set and found that there are total of 16000 neutrinos. That means they dont actually have the ability to tell when a particular neutrino is created. What they did is they compared the distribution of times when they detect neutrinos to the distribution of times when neutrinos were created in the source. They used the fact that neutrinos should comeout from the protons in their original beam. They argue that the distribution of arrival times of the the neutrinos ought to have the same shape as the distribution of arrival times of the protons. There are lots of uncertainties involved and they say that they have accounted for all of them. But clearly somewhere something went wrong.