At my current company, as an employee, I have 4 people I could call 'manager' and I'm not even talking about higher level managers and VPs.
I agree that being a 1099 hired gun can spare you from a lot of politics. It's nice to have a list of tasks the customer wants, bang them out, and walk away with a satisfied customer and a pile of money.
That said, I spent over half my career at two companies which did everything from staff augmentation to full product development. In my experience I did not detect a level of politics comparable to that at a large valley company. Granted, those companies were outside the valley and owned/run by a very smart, personable, experienced leader/engineer/salesman. It helps to do the investigative work up front and define success criteria in the initial statement of work. A lot of customers balk at paying for the upfront work, but it was a pretty firm requirement when you wanted us to take on a project. I was lucky to get hired into a design services firm early on and benefitted from the wisdom of a building full of independent contractors working for an engineering for hire company.
But, like I was getting at originally, I think it varies. There are some types of work that are hard to scope initially or where the customer exhibits child-like behavior. If you can, you can learn to identify those situations and avoid them. It helps when employment is tight and you can turn down work.