Here's another take on the title:

I was told that they are called Fake Books, because with a simple melody line and chords....a musician could "fake" an arrangement without really having a full score in front of him.
That explaination makes more sense to me, although it's true - they always were illegal because they didn't obtain the copyrights back then. Might be different today, but I still think the term refers to the ability to fake it till you make it !