"The Source of Healing The Saviour in His miracles revealed the power that is continually at work in man's behalf, to sustain and to heal him. Through the agencies of nature, God is working, day by day, hour by hour, moment by moment, to keep us alive, to build up and restore us. When any part of the body sustains injury, a healing process is at once begun; nature's agencies are set at work to restore soundness. But the power working through these agencies is the power of God. All life-giving power is from Him. When one recovers from disease, it is God who restores him. MH 112"
"For in him we live, and move, and have our being; as certain also of your own poets have said, For we are also his offspring."
The EGW passage directly echoes the sentiment of Acts 17:28, emphasizing God as the source of life and being, and expanding on it in the context of healing.
"Who forgiveth all thine iniquities; who healeth all thy diseases;"
Both passages connect God with healing. The Psalm speaks directly of God healing diseases, while EGW speaks of God's power restoring health.