Moderators on reddit have 1) full control of their subreddit and only have a few basic guidelines/rules to follow but basically they can do/ban what/who they want 2) are not paid.

This is correct. I started r/cubancigars for example. It's mine. I can kick every single moderator off the team, shut the sub down, or change the rules without care. I don't, but I can, and nobody would stop me.

MisterBastahrd : r/cubancigars :: Zuck : Facebook

This comment sounds exactly like something a stereotypical cigar smoker would say.

No, my comment illustrates the basic facts of being the top moderator on a subreddit.

If I'm not breaking reddit rules, then as long as I've been active any time within the past 6 months, I own the subreddit and can make changes to the direction of the sub and its moderation team as I see fit.

That subreddit was created, by the way, because I disagreed with rules regarding the discussion of Cuban cigar sources which ship to the US in the main cigar subreddit. They're free to administer their subreddit as they see fit, and I'm free to do the same.

The moderators on Reddit and stack overflow aren't paid, and broadly set their own guidelines.

Anyone with enough points on SO becomes a mod automatically, and gets to deal with "how dare you close my shitty off topic question, I have every right not to follow the rules and homogenise so into every other discussion forum". Anyone who starts a subreddit becomes the mod of it and can promote other mods at will.