(first, sorry for my slow response, and thank you very much for catching this!)
Yes, you are right. This sentence is really terribly wrong! (I'm not sure how this error has escaped detection for so long!)
It is certainly true that you are reflecting off of G n. And if G corresponds to some lattice spacing d, then Gn corresponds to a spacing d/n. And as you say, unless G is the shortest recip latt vector in a given direction, then it does not correspond to a family of lattice planes.
What is true is that if you have a wave with wavelength (2 d sin theta)/n you can still reflect off of a family of lattice planes with spacing d.
Sorry for the confusion!