How did Joseph Smith manage to heal the sick?

Joseph Smith performed many miracles of healing throughout his life such as healing the sick in Nauvoo, healing Joseph Smith’s father, healing Angeline Works and the miracle reported by Fanny Stenhouse after her apostasy from the Church

Keith Perkins reports another miracle healing experienced in 1831:

In that year John and Elsa also went to Kirtland to see the Prophet and to find out more about the new religion. During the visit a healing occurred which caused a great stir in the area. Elsa Johnson had been afflicted for many years with a rheumatic arm. She experienced so much pain and difficulty in movement that for two years she hadn’t been able to raise her hand to her head. As the Johnsons and others from the Hiram area visited with Joseph Smith in the Newel K. Whitney home, they discussed the gifts of the Spirit as held in the early Church. Someone asked whether God had given power to men today to heal people like Elsa Johnson. After the conversation had turned to another subject, the Prophet walked up to Elsa and said, “Woman, in the name of the Lord Jesus Christ I command thee to be whole,” and then he walked out of the room. Elsa was instantly healed, and the next day she did her washing “without difficulty or pain.” (See History of the Church, 1:215–16.) This experience was instrumental in the conversion of a number of people, including Father and Mother Johnson (as they were affectionately called by the Saints), and their children John, Jr., and Marinda.
– Keith Perkins – A House Divided: The John Johnson Family

Was this experience just a coincidence? Why would Elsa immediately stretch out her arm straight, remarking it’s as well as the other? How was Joseph able to do these things if it were not by Christ’s priesthood?

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