Understanding social hierarchy is a skill that can be learned and you can raise your position in that hierarchy using that skill.
When people say "I'm not political" they're really just confessing to low social status and acumen. I personally wish things were different, but as you note they're not. So one may as well accept reality and play the game as best as one can. One can have a very successful career as a follower if one recognizes the traits of good leaders and the traits that good leaders are looking for.
Maybe. They could be fearing being disliked, estranged, or an argument for having the "wrong" beliefs. (Politics, religion, computer languages.)
Much like gossip, politics is pack violence and order by other means, and is usable by people who have less physical power but more social influence. If you don't have either physical and social power, then you're dismissed as not a threat and ripe to be stepped-on. Gossip is often a political attack technique to take-down a physically-strong leader.
I would agree that almost all companies are political to some degree, but I wouldn't agree with heavily political. It's a sign of poor leadership if they end up in that state because you can minimize the impact of different goals and incentives, be they personal, professional, or organizational which is what drives basically all of politics.
