  We rebut the recent claim (arXiv:0912.5463) that Einstein-frame scattering in
the Higgs inflation model is unitary above the cut-off energy Lambda ~ Mp/xi.
We show explicitly how unitarity problems arise in both the Einstein and Jordan
frames of the theory. In a covariant gauge they arise from non-minimal Higgs
self-couplings, which cannot be removed by field redefinitions because the
target space is not flat. In unitary gauge, where there is only a single scalar
which can be redefined to achieve canonical kinetic terms, the unitarity
problems arise through non-minimal Higgs-gauge couplings.
