I was reading this note by Jingzhou Sun http://arxiv.org/abs/1109.1329 about Demailly's approach to hyperbolicity using jet differentials. The author seems to claim that there is a mistake in one of Demailly's early papers on the subject, and even shows a calculation that apparently contradicts a classical result of Demailly-El Goul (and potentially many other later works based on this approach).

More specifically, he claims that there are two definitions of the bundle of $k$-jet differentials of weighted degree $m$ which people assumed were equivalent, but which in fact are not the same.

Has anybody looked at this note? Is the objection raised by the author justified?