I'm 100% sure you're correct, but if you think about it, there are restrictions on that URFA who's contract expired as opposed to terminated.
Let's take Cory Proctor, for example. His contract will expire in March, if it hasn't already. Now let's say Proctor wants to sign with the Saints, and the Saints want to sign him ( Please, Lord, make it so... but I digress ). However, under the rules, until the Saints lose a player of their own, who's contract has expired too, they're prevented from signing Proctor. If the Saints don't lose one of those players, they cannot sign Proctor during the FA period and Proctor cannot sign with them even if he wanted to.