However, the essence of the matter isn't just about putting you in a cage - it's about excessive and capricious penalties with no real recourse. And those exist aplenty in the private sector. Nor do all laws broken necessarily equate to imprisonment.
In practice, for perceived infractions against whatever rules the powerful organization has, private organizations are pretty ruthless up to but not quite reaching imprisonment. Pseudo-monopolists cutting service, or hefty financial penalties up to and including losing pretty much everything, holding your data hostage: that's all fair game.
These two things aren't the same; but I do think they're both bad and scary enough to warrant not just concern, but in an ideal world, rules. You know, for example, constraints for government, and licensing rules for business.
Historically speaking this is completely false. Even now you can find individual examples of businesses doing things like this, especially in places with little rule of law.
There is nothing magical about businesses - they are made up of the same people that make up governments. Those people have the same power trips regardless of their positions.