Why immutable singleton has no global state?

In an article called Root Cause of Singletons writed by Miško Hevery:

Now, there is one kind of Singleton which is OK. That is a singleton where all of the reachable objects are immutable. If all objects are immutable than Singleton has no global state, as everything is constant.

A singleton always has global state, because all of the design patterns of singleton expose a global reference to the single instance.

But why immutable singleton has no global state?