There is no avoiding office politics. Even an employee who 'avoids' politics, doesn't speak up and does not network, is taking a part in office politics, that of the 'naive' employee, as expressed in Chapter 15. A sensible employee will learn to work the system and realize that politics can actually be beneficial if handled correctly. If politics is abused, then corruption occurs. Employees that view the politics of their company as an opportunity, but do not balance their acts with morals, then they are called 'sharks' and are not well liked by other employees.
An article I found talked about how to win at office politics. The most important thing is to network and build relationships- not just with the people above you who can get you promoted, but with those below you. You want to be able to get along with everyone. One of the metaphors the author used was of high school. A good student would do what they were told and complete assignments, however the students that became the teacher's 'pet' and whose names their teachers remembered the next year were those that went above and beyond what was expected of them on projects and spoke up in class discussions or asked for extra help after class. It is the same principle in the business world. You cannot be afraid of 'using' people. You have to go in with your whole attitude and energy and put yourself up there (for the better or the worse). A naive person to how politics works and keeps their head down will never climb the corporate ladder. It is all about who you know and how you present yourself.