The purpose of linking a private blockchain (Mijin) to a public blockchain (NEM) is for immutability. A private blockchain has a central authority which can alter that blockchain at their discretion. Linking it to a public chain which is immutable due to it's decentralized nature solves that problem and you get best of both worlds.
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. 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.
Running it on a multitude of nodes does not make something decentralized if you control all of those nodes.
I guess the idea with linking is that you can make it decentralized without handing out control over your nodes, thus keeping control over your own chain while it is still immutable.