While this is essentially true, It is really true when involving Catholic/Christian persons in a failed marriage as you described. But in the case of non-Christians in a marriage that fails, all of that is not required for the Pauline Privilege to be invoked so that the the non-Christian could marry a Catholic in the Church
The devil is in the details. If a Catholic marries a non-Catholic in an invalid marriage, then if they divorce, not only is the Catholic free to marry in the Church, but also the non-Catholic…Because the entire marriage was invalid.