RCinFLA, you neatly summarized the book.
Other books have somewhat different versions, though.
What is really true however, was that Shockley (a genius with a famously difficult temper) did not get along well with Brattain and Bardeen. Thus two camps have arised: those who give the credit mostly to Shockley, and those who give the credit mostly to Bardeen and Brattain. The truth may be that each individual contribution (whether large or small) actually solved a piece of the puzzle.
In the end, all three were recognized by the Nobel prize comitee.