It is my understanding that you can have a Catholic burial as long as you haven’t been formally excommunicated by the Church and didn’t have the excommunication revoked. As in Post #2, the priest performs a Mass of Catholic burial because no one knows what reparations the deceased made before dying except God or his/her confessor.
You're correct. In the case of Ted Kennedy, we do know the name of his confessor.
We have no idea if Senator Kennedy had a deathbed re-conversion. We cannot judge.
Beginning Catholic: The Anointing of the Sick: Comfort and Healing [Ecumenical]