  We comment on the claim by Lebedev and L'vov [arXiv:1005.4575] that the
symmetry with respect to a tilt of a quantized vortex line does not yet
prohibit coupling between Kelvin waves and the large-scale slope of the line.
Ironically, the counterexample of an effective scattering vertex in the local
induction approximation (LIA) attempted by Lebedev and L'vov invalidates their
logic all by itself being a notoriously known example of how symmetries impose
stringent constraints on kelvon kinetics---not only the coupling in question
but the kinetics in general are absent within LIA. We further explain that the
mistake arises from confusing symmetry properties of a specific mathematical
representation in terms of the canonical vortex position field w(z) = x(z) +
iy(z), which explicitly breaks the tilt symmetry due to an arbitrary choice of
the z-axis, with those of the real physical system recovered in final
expressions.
