"Once a year, on the great Day of Atonement, the priest entered the most holy place for the cleansing of the sanctuary. The work there performed completed the yearly round of ministration. On the Day of Atonement two kids of the goats were brought to the door of the tabernacle, and lots were cast upon them, “one lot for the Lord, and the other lot for the scapegoat.” Verse 8 . The goat upon which fell the lot for the Lord was to be slain as a sin offering for the people. And the priest was to bring his blood within the veil and sprinkle it upon the mercy seat and before the mercy seat. The blood was also to be sprinkled upon the altar of incense that was before the veil. GC 419.1"
"And he shall make an atonement for the holy place, because of the uncleanness of the children of Israel, and because of their transgressions in all their sins: and so shall he do for the tabernacle of the congregation, that remaineth among them in the midst of their uncleanness."
The EGW passage directly quotes and explains Leviticus 16, accurately describing the Day of Atonement rituals.
"the man who led him away was required to wash himself and his clothing with water before returning to the camp. GC 419.2"
"And he that let go the goat for the scapegoat shall wash his clothes, and bathe his flesh in water, and afterward come into the camp."
The EGW passage is a direct reference to and explanation of Leviticus 16:26.