Surplus Efficient Frontier

In Example 14, p241, vol. 4, they give a nice explanation of why T-Bills don’t appear in any portfolio on the surplus efficient frontier of the example’s fully-funded pension plan. Then, in Example 15, when the plan becomes underfunded, the stated policy mix (which includes T-Bills) suddenly does plot on the surplus efficient frontier. Why is that? It would seem to me that the same considerations that prevented T-Bills from being efficient in the fully-funded case would also apply in the underfunded case.