How to check private state in unit testing?

I have read some discussions on the internet. They say that we should not unit test private methods or check private state because that's implementation detail and a sign of bad design. But in my case, I really don't know how to do better.

Here is an example code (my actual code is angular using factory, but I try to create a same case using plain js so that everyone is easier to understand because the same cause is closure):

function closure(){
    var state = {};

    return {
        refreshState : function(property1,property2) {
            state.property1 = property1;
            state.property2 = property2;

            //store these properties into localstorage
        },
        getState: function () {
            if (!state.property1) {
                state.property1 = //retrieve from localstorage
            }
            if (!state.property2) {
                state.property2 = //retrieve from localstorage
            }
            return state;
        }
    };
};

var objectToTest = closure();

In my real app, I can inject and mock the local storage, but it's a question here. My question is how to test that the refreshState method sets its private state because I cannot verify its value:

state.property1 = property1;
state.property2 = property2;

I'm thinking about stubbing the local storage and use the getState method to get the state. But it looks like integration test because the getState has its own logic that I cannot get rid of.