On November 18th, 2011, I wrote about the invalid paper by Pusey et al.
First, you should replace "to proof" by "to prove" twice in the paper, to avoid irritation by this imperfection of the author's English. ;-)
In the second sentence of the abstract, Hofmann already points out that Pusey et al. implicitly assume that the natural phenomena have to be reflections of some hidden variable model. They assume that the observations are reflections of some objective reality. You may remember I said the same thing: they are trying to settle an "ontic vs. epistemic" battle, not realizing that both "ontic" as well as "epistemic" camps (of hidden variable advocates) have been known to be wrong at least for half a century. Hofmann says many comments about the need to treat physics in a positivist way and only accept that the results of observations are "real".
One of the things he proves in the main text and in the final note  is that the authors are dogmatic. Hofmann, being perfectly polite, adds that by "dogmatic", he doesn't mean that they're narrow-minded. But he has the duty to kindly point out that their blind belief unsupported by the evidence is more similar to that of Christian bigots and Islamic fundamentalists than what some physicists are ready to admit – which may be dangerous. ;-)
Holger Hofmann seems to be a pretty successful researcher in the foundations of quantum mechanics, given the fact that what he writes is actually valid. But these features may have something to do with his Japanese affiliation (or exile?).
The short paper has a "constructive" portion, too. He shows that one may interpret the density matrix as a statistical distribution and in a similar way as Pusey et al. did – by using the methods of the Wigner function. The agreement with the quantum mechanical predictions is guaranteed and the paradox is avoided – despite this "seemingly classical interpretation" – by the fact that the probabilities encoded in the density matrix in this way may be negative. However, that doesn't lead to actual negative "frequencies" how often a certain outcome is measured because these negative probabilities only refer to joint properties of the system that can't be measured simultaneously.
So thankfully, I just learned that there are theorists who are mainly working in "quantum foundations" who are not completely deluded when it comes to the meaning of quantum mechanics.