There needn't be any massless particles at all for SR to be valid. Also, SR is compatible with tachyons (not implying that neutrinos may be tachyons). I would think that either causality or the 0 mass of a photon would be more at risk than SR from a confirmation of this result.Isn't this forgetting about the connection between EnM and SR, though. I think that connetion pretty much says the photons of EnM have to be the massless particles of SR. The "c" in SR cannot apply to a particle with mass, or the invariance is lost, and the whole theory goes to cr@p.
That said, I would really like to see the actual scientific publication rather than a pop-media report.