Thanks for the explanation. If I understand correctly, it is still up to the company running the private blockchain to decide whether or not they want to leverage the public blockchain by linking the two.
Yes, not all private chains will want immutability but many will which is a very valuable feature.
Immutability in this case could still be achieved by running the private blockchain on multitude of nodes effectively making them decentralizedalthough it would not be as reliable as linking to a public blockchain.
In a private blockchain, a single entity controls all of the nodes so they would be able to change the blockchain at their discretion so immutability is not possible without a decentralized public block chain to anchor to.