I think I've just realised the wisdom in Nick's and Waspy's comments about relating drag to the free stream.
I'm guessing the aerodynamicists definition of induced drag is quite narrow, ie. the cost of tip vortex production in the direction of the free stream. Therefore without tip vortices (ie with an unbounded wing) there can be no induced drag as far as an aerodynamicist is concerned.
I'm further guessing that Prouty, Wagtendonk et al and anyone else responsible for educating pilots may have appropriated the term induced drag to cover ANY gain in ROTOR drag as a result of lift production from the pilot's perspective.
If my guesses are correct the circle is squared, and everybody can be right according to their different definitions.