In our earlier post we discussed why this bound they put forward was based on a weak argumentation. The essential point was assuming the highest energy photon had been emitted during a particular late peak in the low energy spectrum. Since that peak almost coincided with the arrival of the photon the resulting bound was very strong. There is however no knowing exactly when the photon was emitted. The most plausible assumption is that it wasn't emitted before the onset of the burst in the low energy regime. This assumption however gives a much weaker bound, pretty much exactly at the Planck scale.
The paper got now published in Nature, but it is significantly toned down from the original claim. The "most secure and conservative new limit" is at 1.2 times the Planck scale. The limit of 102 times the Planck scale that arises from associating the 31-GeV photon with the 7th spike is still offered, but explained to be "not very secure." Seems to me the referees did a good job...
The topic even made it into the New York Times. Dennis Overbye writes that 7.3 Billion Light-Years Later, Einstein’s Theory Prevails, and quotes the eternally optimistic Lee Smolin:
The good news, astronomers said, is that more data expected from Fermi could decide the question. As Lee Smolin, a quantum gravity theorist from the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, said, “So a genuine experimental test of a hypothesized quantum gravity effect is in progress.”
New Scientist reports on Giovanni Amelino-Camelina's stomach aches, and SymmetryMagazine explains the why and how in a very recommendable article Gamma-ray burst restricts ways to beat Einstein’s relativity.
For more details, see also our earlier post Constraining Modified Dispersion Relations with Gamma Ray Bursts.