"Remedial Agencies Those who seek healing by prayer should not neglect to make use of the remedial agencies within their reach. It is not a denial of faith to use such remedies as God has provided to alleviate pain and to aid nature in her work of restoration. It is no denial of faith to co-operate with God, and to place themselves in the condition most favorable to recovery. God has put it in our power to obtain a knowledge of the laws of life. This knowledge has been placed within our reach for use. We should employ every facility for the restoration of health, taking every advantage possible, working in harmony with natural laws. When we have prayed for the recovery of the sick, we can work with all the more energy, thanking God that we have the privilege of co- operating with Him, and asking His blessing on the means which He Himself has provided. GW 220"
"But when Jesus heard that, he said unto them, They that be whole need not a physician, but they that are sick."
Both passages address the use of medical means in conjunction with faith/prayer. Matthew 9:12 implies that the sick need a physician, while the EGW passage explicitly states that using remedial agencies is not a denial of faith and encourages cooperation with natural laws. The connection is thematic, dealing with the relationship between faith and medical treatment.
"We have the sanction of the word of God for the use of remedial agencies. Hezekiah, king of Israel, was sick, and a prophet of God brought him the message that he should die. He cried unto the Lord, and the Lord heard His servant, and sent him a message that fifteen years should be added to his life. Now one word from God would have healed Hezekiah instantly; but special directions were given, “Let them take a lump of figs, and lay it for a plaster upon the boil, and he shall recover.” [ Isaiah 38:21 .] GW 220.2"
"For Isaiah had said, Let them take a lump of figs, and lay it for a plaister upon the boil, and he shall recover."
The EGW passage directly quotes and references Isaiah 38:21, making it an explicit allusion.
"And Isaiah said, Take a lump of figs. And they took and laid it on the boil, and he recovered."
The EGW passage is explicitly alluding to the event described in 2 Kings 20:7, which is the same event described in Isaiah 38:21. The reference to Hezekiah and the figs makes the connection undeniable.