Actually, the Book states that Gollum DID bite off Frodo's finger.

Also, it does state that Shelob stings Frodo, and it also states that Sam interrupts Shelob's cocooning him. After Sam gets rid of Shelob, Frodo is carried off by the Orcs to the Tower of Cirith Ungol.

If you're going to get all angry about something, plz know what you are talking about.