I do not think so. Extreme Unction is the same kind of thing as Baptism. If you agree that grace can be given by the application of water in Baptism, as you do, you should find no difficulty in admitting that grace could be given by the application of oil, should the same Christ decide to institute such a Sacrament.
Radio Replies Volume 1 by Rev. Dr. Leslie Rumble MSC and Rev. Charles Mortimer Carty