Maybe "insolvent" is the wrong word. But I consider something to be insolvent when its liabilities exceed its assets. You would probably use the word "underfunded" for this. For about 30% of the time, the liabilities exceed the assets.
What are the liabilities?
The smoothed value is not the liability. The liability, or obligation if you like, is to deliver the benefits as determined by the smoothing formula and of course the rules of entry and exit. This can only be tested by stochastic methods and the paper goes to some lengths to explain how the formula withstands such a test.