  The partial Hamiltonian analysis of the actions presented in the paper by M.
Chaichian, M. Oksanen, A. Tureanu (Eur. Phys. J. C 71, 1657 (2011)) is
incorrect; the true algebra of constraints differs from what they claim for
their choice of momentum constraint. Our blind acceptance of the correctness of
their constraint algebra led us to conclude, wrongly, that a few of the models
presented by the authors (sharing the same constraint algebra) are not
invariant under spatial diffeomorphism. We "proved" this by using Noether's
second theorem (see first version of the paper), but we then found a mistake in
our calculations. The differential identity of spatial diffeomorphism is
intact, therefore, their actions are invariant; but in this case, the spatial
diffeomorphism gauge symmetry cannot be compatible with their algebra. We now
explicitly demonstrate that the actual algebra of constraints is different, and
briefly describe how it affects the generator and gauge transformations of the
fields.
