Yes, but with more energy they should be even closer to c if they have slight mass. That is what Minos shows, i.e. very close to c, and not readily distinguishable from c within the accuracy of the experiment.
Somehow, Gran Sasso believes that increasing the energy from SN1987A levels, in which the speed is at or below c, with an increase by a factor of 100, would magically make them cross the c-barrier.
In other words, according to the Gran Sasso 'results', one would expect even higher energy neutrinos to continue at speeds well above c, directly contradicting Einsteinian physics which equates increasing energy with increasing relativistic mass the closer one gets to c, but never crossing c.
And, as mentioned, the Minos data has highly energetic neutrinos too, and they do not report a variation as far from c as does Gran Sasso (1/40,000), but rather a variation from c that could be entirely accountable due to their errors of timing, etc., and comparable to the SN1987A range (1/490,000,000).
I suspect that is why several researchers refused to sign on to the Gran Sasso report, as per the last paragraph of the article here:
http://www.guardian.co.uk/science/life-and-physics/2011/sep/24/1?commentpage=3#start-of-comments
The last paragraph reads: "
I received a comment on this piece from Luca Stanco, a senior member of the Opera collaboration (who also worked on the ZEUS experiment with me several years ago). He points out that although he is a member of Opera, he did not sign the arXiv preprint because while he supported the seminar and release of results, he considers the analysis "preliminary" due at least in part to worries like those I describe, and that it has been presented as being more robust than he thinks it is. Four other senior members of Opera also removed their names from the author list for this result. He wished to comment, and agreed to me adding this text."
Apparently, the author of the Guardian article used to work with Stanco, and was contacted by him to express his displeasure at the premature publication.