Thank you for a great reply!

I'm still very curious to learn more about different private blockchains so if anyone has some links that explain how they work in-depth, I would be very grateful if you post it here.

I also have some more questions:

1. Are all private blockchains permissioned or what makes a blockchain private?

2. If a private blockchain has only one permissioned entity that can append new blocks ("miner") and it doesn't do any PoW or PoS, how close this entity becomes to a traditional middleman? I understand that they can't alter transactions is they are signed by digital signatures, but what they can possibly do?

3. Are they vulnerable to some attacks that don't exist in decentralized blockchains?