All of the authors atyy cites believe that spin-2 field theory is identical to GR in physical predictions at least up to the event horizon, and possibly beyond (except, of course, for Hawking radiation). Baryshev believes that spin 2 field theory predicts that the event horizon doesn't exist, and therefore that Bekenstein-Hawking thermodynamics of black holes is incorrect. You can see this more clearly from some of Baryshev's other papers.
See, for example: http://arxiv.org/abs/0809.2328
Almost all other authors on spin 2 field theory would disagree with every prediction of the above paper, believing that spin 2 field theory would agree with GR instead. As with atyy, I am not in a position to judge Baryshev on the merits.
One comment on the disagreement is noted in the following:
"Finally, let us mention that approaches exist that treat gravity as simply a spin-2
flat space [114, 115]. It has been conjectured that one could reconstruct the
Einstein-Hilbert action in such an approach by considering consisitency conditions order
by order in perturbation theory. This will, of course, be an invalid treatment when
gravity is strong, and in cosmology."
Most authors disagree with this paragraph and argue that such recovery of the Einstein-Hilbert action is imperative, and that the comment on invalidity is itself invalid.