  We reexamine the tunneling density of states in quantum dots and
nanoparticles within the model which is extension of the universal Hamiltonian
to the case of uniaxial anisotropic exchange. We derive the exact analytical
result for the tunneling density of states in the case of arbitrary
single-particle energy spectrum. We find that, similar to the case of the
isotropic exchange, the tunneling density of states as a function of energy has
the maximum due to a finite value of the total spin of the ground state near
the Stoner instability. We demonstrate that there are no additional extrema
which have been predicted on the basis of perturbative analysis [M.N. Kiselev
and Y. Gefen, Phys. Rev. Lett. {\bf 96}, 066805 (2006)].
