"The "brief note" is a commentary, also published in the Vatican newspaper, which explains that "in these last decades theological tendencies have been manifested that cast doubt on the Doctrine of the Church, according to which the minister of the Sacrament of the Anointing of the Sick 'est omnis et solus sacerdos,'" in keeping with the formulation of the Council of Trent (1542-1563)."
in keeping with the formulation of the Council of Trent (1542-1563)... insist on Extreme Unction.
Catholics often carry cards in their wallets, or wear medals around their necks, that contain the above words (or simply, "I'm Catholic; call a priest"), sometimes with the priest's phone number/pager number. These cards are meant to help ensure that in an emergency, a doctor, nurse, EMT, policeman, etc., will call a priest to administer Unction to the Catholic in need. Make sure that family members, even non-Catholic ones, are aware of your desire for Unction if you are facing death, and have your priest's phone number/pager number someplace where they'll be able to locate it easily.