My impression was that the original 'fake' books were bootleg collections of songs, often with just sufficient lyrics, score and lyrics to enable the reader to play the material - certainly not a full piano score. They sold like hot-cakes and of course paid no royalties to either composers or contracted publishers.

At that time conventional publishers would put together a few good songs - combined with a fair amount of crap - and publish them as a small compendium (at outrageous prices). They were not offering the market what it wanted, so then followed suit with 'real fake'books from their own stable of copyright material. They cut down on the extraneous parts of the score - which the new market either couldn't or wouldn't read, increased the content of popular songs and sold them at a price that was more affordable. They stole the 'fake' brand name because the market associated it with good value. End of Marketing 101, as I view it.

Regards, John