Fake Counterpoint

There's a term, "fake counterpoint", that I believe I picked up from Douglas Leedy, and recently noticed in a blog item by composer Paul Bailey. When I use the term, I refer to an ensemble texture that appears, initially, to be composed of multiple, differentiated, lines, but on closer inspection turns out to be a single line distributed onto an ensemble via doublings, octave doublings, simultaneous variations, and sometimes slight delays or "Japanese canons"*, loosely creating an illusion of "real counterpoint". It's something that's clearly related to ensemble practice in much non-classical music** (the opening to Renard imitates such a texture). I find "fake counterpoint" to be particularly useful in my own music, as a texture of its own, and as one intermediate to a single melody and an ensemble of different melodies.

Can anyone out there can help me locate the origins of the term?

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*Henry Cowell's term, picked up by Cage and Harrison and their students, derived from the Hichirichi playing in the introductory, Netori section of some Gagaku repertoire in which the instruments are loosely alligned and can move ahead or behind one another.
**In school, you might have encountered the term "heterophonic",and it may or may not have been correctly applied. In systematic musicology, ensemble textures are described quantitatively as monophonic or polyphonic, and the individual lines in an ensemble are characterized as similar ("homophonic") or differentiated ("heterophonic"). These descriptions necessarily represent continua, and real musics have relative, not absolute positions in them.