I think there are two possible explinations as to why they are called fake books.

1. All you get is a lead line and chord symbols. You have to make up the arrangement on the fly. In other words you are faking (making up) everything except the melody.

2. Some (most) of these books were illegal. They violated most copyright laws because the publisher of these books did not have permission from the copyright holder to use the songs. No royalities were paid to the composer.

Maybe Don or Uncle Dave can shed some more light on the subject.

Tom