And more than ever believers were added to the Lord, multitudes both of men and women, so that they even carried out the sick into the streets, and laid them on beds and pallets, that as Peter came by at least his shadow might fall on some of them.
There are charisms of healing and then there is the sacrament of Anointing. One can have a charism of healing without being ordained. One can be ordained without having a charism of healing. But one cannot administer the sacrament of Anointing without being ordained. That's because the sacrament is a direct action of Christ through his Holy Church. When Peter's shadow fell on people and healed them, or when handkerchiefs touched by Paul healed people in Ephesus (Acts 19:11-12), this was not the sacrament of anointing which James 5:14-15 describes. It was a charism, a spiritual gift given for the building up of the body. The sacraments depend, not on the specific charism of a specific person, but on the grace of Christ promised the Church through the power of the Holy Spirit. The priest conferring the sacrament stands, not in his own place enacting a personal gift, but in the place of Christ and with not reference to his own person. This means, happily, that any priest will do in the sacrament of Anointing since it does not matter what his talents, insights, gifts, moral state, intelligence, or savoir faire might be. All that matters is that Christ guarantees to be at work in the sacrament. And that's what we need, praise God!