Thanks. I guess we are interested in the power, since that is what we measure. So I get
cos(ωt) . cos(ω+Ω)t = ½[cos(Ωt) + cos(2ω+Ω)] and
cos(ωt) . cos(ω-Ω)t = ½[cos(Ωt) + cos(2ω-Ω)].
Adding them and keeping terms at Ω gives cos(Ωt), so I get a nonzero DC-signal. Is the author wrong then?