  The Casimir friction problem can be dealt with in a simplified way by
considering two harmonic oscillators moving with constant relative velocity.
Recently we calculated the energy dissipation for such a case, [EPL {\bf 91},
60003 (2010); Europ. Phys. J. D {\bf 61}, 335 (2011)]. A recent study of Barton
[New J. Phys. {\bf 12}, 113044 (2010)] seemingly leads to a different result
for the dissipation. If such a discrepancy really were true, it would imply a
delicate difficulty for the basic theory of Casimir friction. In the present
note we show that the expressions for the dissipation are in fact physically
equivalent, at T=0.
